Foundational-Math-2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "view-in-github"
   },
   "source": [
    "<a href=\"https://colab.research.google.com/github/edatfreecodecamp/python-math/blob/main/Foundational_Math_2_(Learn).ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "EsfO5Q92tL-6"
   },
   "source": [
    "[![freeCodeCamp](https://cdn.freecodecamp.org/testable-projects-fcc/images/fcc_secondary.svg)](https://freecodecamp.org/)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "7ECUmRBSGOb4"
   },
   "source": [
    "**Learn Foundational Math 2 by Building Cartesian Graphs**<br>\n",
    "Each of these steps will lead you toward the Certification Project. Once you complete a step, click to expand the next step."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "szp5flp1fA8-"
   },
   "source": [
    "# &darr; **Do this first** &darr;\n",
    "Copy this notebook to your own account by clicking the `File` button at the top, and then click `Save a copy in Drive`. You will need to be logged in to Google. The file will be in a folder called \"Colab Notebooks\" in your Google Drive. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "iNcDJ45bGtYk"
   },
   "source": [
    "# Step 0 - Acquire the testing library"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2_U7sdv4zaww"
   },
   "source": [
    "Please run this code to get the library file from FreeCodeCamp. Each step will use this library to test your code. You do not need to edit anything; just run this code cell and wait a few seconds until it tells you to go on to the next step."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "aDuDRHETG3Oy",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: requests in c:\\users\\srudr\\appdata\\local\\programs\\python\\python311\\lib\\site-packages (2.28.2)\n",
      "Requirement already satisfied: charset-normalizer<4,>=2 in c:\\users\\srudr\\appdata\\local\\programs\\python\\python311\\lib\\site-packages (from requests) (3.1.0)\n",
      "Requirement already satisfied: idna<4,>=2.5 in c:\\users\\srudr\\appdata\\local\\programs\\python\\python311\\lib\\site-packages (from requests) (3.4)\n",
      "Requirement already satisfied: urllib3<1.27,>=1.21.1 in c:\\users\\srudr\\appdata\\local\\programs\\python\\python311\\lib\\site-packages (from requests) (1.26.15)\n",
      "Requirement already satisfied: certifi>=2017.4.17 in c:\\users\\srudr\\appdata\\local\\programs\\python\\python311\\lib\\site-packages (from requests) (2022.12.7)\n",
      "Code test Passed\n",
      "Go on to the next step\n"
     ]
    }
   ],
   "source": [
    "# You may need to run this cell at the beginning of each new session\n",
    "\n",
    "!pip install requests\n",
    "\n",
    "# This will just take a few seconds\n",
    "\n",
    "import requests\n",
    "\n",
    "# Get the library from GitHub\n",
    "url = 'https://raw.githubusercontent.com/edatfreecodecamp/python-math/main/math-code-test-b.py'\n",
    "r = requests.get(url)\n",
    "\n",
    "# Save the library in a local working directory \n",
    "with open('math_code_test_b.py', 'w') as f:\n",
    "    f.write(r.text)\n",
    "\n",
    "# Now you can import the library\n",
    "import math_code_test_b as test\n",
    "\n",
    "# This will tell you if the code works\n",
    "test.step01()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ZWDxpIPUFfda"
   },
   "source": [
    "# Step 1 - Cartesian Coordinates"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "eTWzFpChFltm"
   },
   "source": [
    "Learn Cartesian coordinates by building a scatterplot game. The Cartesian plane is the classic x-y coordinate grid (invented by Ren$\\acute{e}$ DesCartes) where \"<i>x</i>\" is the horizontal axis and \"<i>y</i>\" is the vertical axis. Each (x,y) coordinate pair is a point on the graph. The point (0,0) is the \"origin.\" The x value tells how much to move right (positive) or left (negaive) from the origin. The y value tells you how much you move up (positive) or down (negative) from the origin. Notice that you are importing `matplotlib` to create the graph. The following code just displays one quadrant of the Cartesian graph. Just run this code to see how Python displays a graph.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "id": "OGdjnZw0Fmf7",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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QDOECACRDuAAAyRAuAEAyhAsAkAzhAgAkQ7gAAMkQLgBAMoQLAJAM4QIAJEO4AADJEC4AQDKECwCQDOECACRDuAAAyRAuAEAyhAsAkAzhAgAkQ7gAAMkQLgBAMoQLAJAM4QIAJEO4AADJEC4AQDKECwCQDOECACRDuAAAyRAuAEAyhAsAkAzhAgAkQ7gAAMkQLgBAMoQLAJAM4QIAJEO4AADJEC4AQDKECwCQDOECACRDuAAAyRAuAEAyhAsAkAzhAgAkQ7gAAMkQLgBAMoQLAJAM4QIAJEO4AADJEC4AQDKECwCQjCGFS1NTU1RVVUVJSUlUV1fH9u3bjzp3w4YNcdFFF8XkyZNj8uTJUVtb+6bzAQCOJu9w2bRpU9TX10dDQ0Ps3LkzZs6cGXV1dfHSSy8NOn/btm1x+eWXx+9///toaWmJysrK+NSnPhV/+9vf3vbmAYCJpSDLsiyfBdXV1XH++efHunXrIiKir68vKisr4/rrr4/ly5e/5fre3t6YPHlyrFu3LhYtWjTonO7u7uju7u7/c2dnZ1RWVkZHR0eUlpbms10AYIx0dnZGWVnZsP78zusZl56entixY0fU1tb+9w4KC6O2tjZaWlqO6T5effXVeP311+Md73jHUec0NjZGWVlZ/62ysjKfbQIA41Re4XLgwIHo7e2N8vLyAePl5eXR1tZ2TPdx4403xvTp0wfEz/9asWJFdHR09N/279+fzzYBgHFq0mhebM2aNbFx48bYtm1blJSUHHVeLpeLXC43ijsDAFKQV7hMmTIlioqKor29fcB4e3t7VFRUvOnaO+64I9asWRO//e1v49xzz81/pwDAhJfXS0XFxcUxe/bsaG5u7h/r6+uL5ubmqKmpOeq622+/PW677bbYunVrzJkzZ+i7BQAmtLxfKqqvr4/FixfHnDlzYu7cubF27dro6uqKJUuWRETEokWLYsaMGdHY2BgREd/97ndj1apV8bOf/Syqqqr63wtz8sknx8knnzyMDwUAGO/yDpcFCxbEyy+/HKtWrYq2traYNWtWbN26tf8Nu/v27YvCwv8+kfPDH/4wenp64rOf/eyA+2loaIhvfvObb2/3AMCEkvf3uIyFkfgcOAAwssb8e1wAAMaScAEAkiFcAIBkCBcAIBnCBQBIhnABAJIhXACAZAgXACAZwgUASIZwAQCSIVwAgGQIFwAgGcIFAEiGcAEAkiFcAIBkCBcAIBnCBQBIhnABAJIhXACAZAgXACAZwgUASIZwAQCSIVwAgGQIFwAgGcIFAEiGcAEAkiFcAIBkCBcAIBnCBQBIhnABAJIhXACAZAgXACAZwgUASIZwAQCSIVwAgGQIFwAgGcIFAEiGcAEAkiFcAIBkCBcAIBnCBQBIhnABAJIhXACAZAgXACAZwgUASIZwAQCSIVwAgGQIFwAgGcIFAEiGcAEAkiFcAIBkCBcAIBnCBQBIhnABAJIhXACAZAgXACAZwgUASIZwAQCSIVwAgGQIFwAgGcIFAEiGcAEAkiFcAIBkDClcmpqaoqqqKkpKSqK6ujq2b9/+pvMfeOCBOOuss6KkpCTOOeec2LJly5A2CwBMbHmHy6ZNm6K+vj4aGhpi586dMXPmzKirq4uXXnpp0PmPP/54XH755XHllVfGrl27Yv78+TF//vx46qmn3vbmAYCJpSDLsiyfBdXV1XH++efHunXrIiKir68vKisr4/rrr4/ly5cfMX/BggXR1dUVv/71r/vHPvrRj8asWbNi/fr1g16ju7s7uru7+//c0dERp512Wuzfvz9KS0vz2S4AMEY6OzujsrIyDh48GGVlZcNyn5PymdzT0xM7duyIFStW9I8VFhZGbW1ttLS0DLqmpaUl6uvrB4zV1dXFL3/5y6Nep7GxMW699dYjxisrK/PZLgBwHPjHP/4xNuFy4MCB6O3tjfLy8gHj5eXlsWfPnkHXtLW1DTq/ra3tqNdZsWLFgNg5ePBgvOc974l9+/YN2wNnaN6oZ89+jT1ncfxwFscX53H8eOMVk3e84x3Ddp95hctoyeVykcvljhgvKyvzD+FxorS01FkcJ5zF8cNZHF+cx/GjsHD4PsSc1z1NmTIlioqKor29fcB4e3t7VFRUDLqmoqIir/kAAEeTV7gUFxfH7Nmzo7m5uX+sr68vmpubo6amZtA1NTU1A+ZHRDz66KNHnQ8AcDR5v1RUX18fixcvjjlz5sTcuXNj7dq10dXVFUuWLImIiEWLFsWMGTOisbExIiJuuOGGuPjii+POO++Myy67LDZu3BhPPPFE3HPPPcd8zVwuFw0NDYO+fMTochbHD2dx/HAWxxfncfwYibPI++PQERHr1q2L733ve9HW1hazZs2K73//+1FdXR0RER//+Mejqqoq7r///v75DzzwQNx8883x4osvxvvf//64/fbb49JLLx22BwEATAxDChcAgLHgdxUBAMkQLgBAMoQLAJAM4QIAJOO4CZempqaoqqqKkpKSqK6uju3bt7/p/AceeCDOOuusKCkpiXPOOSe2bNkySjsd//I5iw0bNsRFF10UkydPjsmTJ0dtbe1bnh3HLt+/F2/YuHFjFBQUxPz580d2gxNIvmdx8ODBWLp0aUybNi1yuVyceeaZ/j01TPI9i7Vr18YHPvCBOPHEE6OysjKWLVsWr7322ijtdvz6wx/+EPPmzYvp06dHQUHBm/4Owjds27YtPvKRj0Qul4v3ve99Az6BfMyy48DGjRuz4uLi7L777sv+/Oc/Z1dffXV26qmnZu3t7YPO/+Mf/5gVFRVlt99+e/b0009nN998c3bCCSdkTz755CjvfPzJ9yyuuOKKrKmpKdu1a1e2e/fu7Itf/GJWVlaW/fWvfx3lnY8/+Z7FG1544YVsxowZ2UUXXZR95jOfGZ3NjnP5nkV3d3c2Z86c7NJLL80ee+yx7IUXXsi2bduWtba2jvLOx598z+KnP/1plsvlsp/+9KfZCy+8kD3yyCPZtGnTsmXLlo3yzsefLVu2ZCtXrsweeuihLCKyhx9++E3n7927NzvppJOy+vr67Omnn85+8IMfZEVFRdnWrVvzuu5xES5z587Nli5d2v/n3t7ebPr06VljY+Og8z/3uc9ll1122YCx6urq7Etf+tKI7nMiyPcs/tfhw4ezU045JfvJT34yUlucMIZyFocPH84uuOCC7Ec/+lG2ePFi4TJM8j2LH/7wh9npp5+e9fT0jNYWJ4x8z2Lp0qXZJz7xiQFj9fX12YUXXjii+5xojiVcvvGNb2Qf/vCHB4wtWLAgq6ury+taY/5SUU9PT+zYsSNqa2v7xwoLC6O2tjZaWloGXdPS0jJgfkREXV3dUedzbIZyFv/r1Vdfjddff31YfxPoRDTUs/jWt74VU6dOjSuvvHI0tjkhDOUsfvWrX0VNTU0sXbo0ysvL4+yzz47Vq1dHb2/vaG17XBrKWVxwwQWxY8eO/peT9u7dG1u2bPElqGNguH52j/lvhz5w4ED09vZGeXn5gPHy8vLYs2fPoGva2toGnd/W1jZi+5wIhnIW/+vGG2+M6dOnH/EPJ/kZylk89thjce+990Zra+so7HDiGMpZ7N27N373u9/FF77whdiyZUs899xz8eUvfzlef/31aGhoGI1tj0tDOYsrrrgiDhw4EB/72Mciy7I4fPhwXHvttXHTTTeNxpb5f472s7uzszP+/e9/x4knnnhM9zPmz7gwfqxZsyY2btwYDz/8cJSUlIz1diaUQ4cOxcKFC2PDhg0xZcqUsd7OhNfX1xdTp06Ne+65J2bPnh0LFiyIlStXxvr168d6axPOtm3bYvXq1XH33XfHzp0746GHHorNmzfHbbfdNtZbY4jG/BmXKVOmRFFRUbS3tw8Yb29vj4qKikHXVFRU5DWfYzOUs3jDHXfcEWvWrInf/va3ce65547kNieEfM/i+eefjxdffDHmzZvXP9bX1xcREZMmTYpnnnkmzjjjjJHd9Dg1lL8X06ZNixNOOCGKior6xz74wQ9GW1tb9PT0RHFx8YjuebwaylnccsstsXDhwrjqqqsiIuKcc86Jrq6uuOaaa2LlypVRWOi/30fL0X52l5aWHvOzLRHHwTMuxcXFMXv27Ghubu4f6+vri+bm5qipqRl0TU1NzYD5ERGPPvroUedzbIZyFhERt99+e9x2222xdevWmDNnzmhsddzL9yzOOuusePLJJ6O1tbX/9ulPfzouueSSaG1tjcrKytHc/rgylL8XF154YTz33HP98RgR8eyzz8a0adNEy9swlLN49dVXj4iTN4Iy86v6RtWw/ezO733DI2Pjxo1ZLpfL7r///uzpp5/OrrnmmuzUU0/N2trasizLsoULF2bLly/vn//HP/4xmzRpUnbHHXdku3fvzhoaGnwcepjkexZr1qzJiouLswcffDD7+9//3n87dOjQWD2EcSPfs/hfPlU0fPI9i3379mWnnHJK9pWvfCV75plnsl//+tfZ1KlTs29/+9tj9RDGjXzPoqGhITvllFOyn//859nevXuz3/zmN9kZZ5yRfe5znxurhzBuHDp0KNu1a1e2a9euLCKyu+66K9u1a1f2l7/8JcuyLFu+fHm2cOHC/vlvfBz661//erZ79+6sqakp3Y9DZ1mW/eAHP8hOO+20rLi4OJs7d272pz/9qf9/u/jii7PFixcPmP+LX/wiO/PMM7Pi4uLswx/+cLZ58+ZR3vH4lc9ZvOc978ki4ohbQ0PD6G98HMr378X/J1yGV75n8fjjj2fV1dVZLpfLTj/99Ow73/lOdvjw4VHe9fiUz1m8/vrr2Te/+c3sjDPOyEpKSrLKysrsy1/+cvbPf/5z9Dc+zvz+978f9N//b/z/v3jx4uziiy8+Ys2sWbOy4uLi7PTTT89+/OMf533dgizzXBkAkIYxf48LAMCxEi4AQDKECwCQDOECACRDuAAAyRAuAEAyhAsAkAzhAgAkQ7gAAMkQLgBAMoQLAJCM/wM9kKRvAVrZIAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Code test Passed\n",
      "Go on to the next step\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "plt.show()\n",
    "\n",
    "# Just run this code to see a blank graph\n",
    "import math_code_test_b as test\n",
    "test.step01()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "i1mBd8gGFvBV"
   },
   "source": [
    "# Step 2 - Cartesian Coordinates (Part 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "aylg20IGFvBW"
   },
   "source": [
    "Here you will create a standard window but still not highlight each axis. Run this code once, then change the window size to 20 in each direction and run it again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "id": "EKfFo4_EFvBX",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n",
      "Code test passed\n",
      "Go on to the next step\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "# Only change the numbers in the next line:\n",
    "plt.axis([-20,20,-20,20]) \n",
    "\n",
    "plt.show()\n",
    "\n",
    "\n",
    "# Only change code above this line\n",
    "import math_code_test_b as test\n",
    "test.step02(In[-1].split('# Only change code above this line')[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "MYQL57cD2ejS"
   },
   "source": [
    "# Step 3 - Graph Dimensions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "b2k229tOz9YQ"
   },
   "source": [
    "When you look at this code, you can see how Python sets up window dimensions. You will also notice that it is easier and more organized to define the dimensions as variables. Run the code, then change just the `xmax` value to 20 and run it again to see the difference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "id": "uXvHo-5a2Zi_",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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POnHihFwuV70/GwgEFAgEgvt+v19paWny+XyKj49v3PAAAKBJ+P1+ud3usDx+hz1mjh49qmPHjp13TWZmpmJiYs46vm3bNvXs2VM7duxQVlbWRd1eOP8wAABA0wjn43fYX2ZKSkpSUlLSr/rZiooKtWrVSsnJyWGeCgAAtFSOvWemvLxcGzdu1MCBAxUXF6fy8nJNmDBBf/zjH9WxY0enxgIAAJZxLGZcLpeWL1+u6dOnKxAIKCMjQxMmTFBxcbFTIwEAAAs5FjN9+vTRhg0bnLp5AADQQjj+PTMAAACNQcwAAACrETMAAMBqxAwAALAaMQMAAKxGzAAAAKsRMwAAwGrEDAAAsBoxAwAArEbMAAAAqxEzAADAasQMAACwGjEDAACsRswAAACrETMAAMBqxAwAALAaMQMAAKxGzAAAAKsRMwAAwGrEDAAAsBoxAwAArEbMAAAAqxEzAADAasQMAACwGjEDAACsRswAAACrETMAAMBqxAwAALAaMQMAAKxGzAAAAKsRMwAAwGrEDAAAsBoxAwAArEbMAAAAqxEzAADAahGLmVmzZql///6KjY1VQkJCvWsqKys1ZMgQxcbGKjk5WY8//rjOnDkTqZEAAEAL1CZSV1xTU6Phw4crJydHr7766lmX19bWasiQIfJ4PFq/fr0OHz6sBx98UNHR0XruueciNRYAAGhhoowxJpI3sGTJEo0fP17V1dUhx99//3399re/1aFDh5SSkiJJWrx4sSZNmqSjR48qJibmoq7f7/fL7XbL5/MpPj4+3OMDAIAICOfjt2PvmSkvL9d1110XDBlJysvLk9/v17Zt2875c4FAQH6/P2QDAACXLsdixuv1hoSMpOC+1+s958+VlJTI7XYHt7S0tIjOCQAAmrcGxczkyZMVFRV13m3Hjh2RmlWSNGXKFPl8vuC2f//+iN4eAABo3hr0BuCJEyeqsLDwvGsyMzMv6ro8Ho8+/fTTkGNVVVXBy87F5XLJ5XJd1G0AAICWr0Exk5SUpKSkpLDccE5OjmbNmqUjR44oOTlZkrRq1SrFx8frmmuuCcttAACAli9iH82urKzUt99+q8rKStXW1qqiokKS1L17d3Xo0EGDBw/WNddcowceeEBz586V1+vV008/raKiIp55AQAAFy1iH80uLCzU0qVLzzq+evVqDRgwQJL09ddfa/To0VqzZo3at2+vESNGaPbs2WrT5uIbi49mAwBgn3A+fkf8e2YijZgBAMA+LeJ7ZgAAAMKBmAEAAFYjZgAAgNWIGQAAYDViBgAAWI2YAQAAViNmAACA1YgZAABgNWIGAABYjZgBAABWI2YAAIDViBkAAGA1YgYAAFiNmAEAAFYjZgAAgNWIGQAAYDViBgAAWI2YAQAAViNmAACA1YgZAABgNWIGAABYjZgBAABWI2YAAIDViBkAAGA1YgYAAFiNmAEAAFYjZgAAgNWIGQAAYDViBgAAWI2YAQAAViNmAACA1YgZAABgNWIGAABYjZgBAABWI2YAAIDVIhYzs2bNUv/+/RUbG6uEhIR610RFRZ21LV++PFIjAQCAFqhNpK64pqZGw4cPV05Ojl599dVzristLVV+fn5w/1zhAwAAUJ+IxcyMGTMkSUuWLDnvuoSEBHk8nkiNAQAAWjjH3zNTVFSkxMRE9evXT6+99pqMMeddHwgE5Pf7QzYAAHDpitgzMxdj5syZuv322xUbG6sPP/xQjz76qE6cOKFx48ad82dKSkqCz/oAAABEmQs9FfIzkydP1pw5c867Zvv27erRo0dwf8mSJRo/fryqq6sveP1Tp05VaWmp9u/ff841gUBAgUAguO/3+5WWliafz6f4+PgLnwQAAHCc3++X2+0Oy+N3g56ZmThxogoLC8+7JjMz81cPk52drWeffVaBQEAul6veNS6X65yXAQCAS0+DYiYpKUlJSUmRmkUVFRXq2LEjsQIAAC5axN4zU1lZqW+//VaVlZWqra1VRUWFJKl79+7q0KGD3nnnHVVVVemmm25S27ZttWrVKj333HN67LHHIjUSAABogSIWM1OnTtXSpUuD+71795YkrV69WgMGDFB0dLQWLlyoCRMmyBij7t27a/78+Ro1alSkRgIAAC1Qg94A3ByF8w1EAACgaYTz8dvx75kBAABoDGIGAABYjZgBAABWI2YAAIDViBkAAGA1YgYAAFiNmAEAAFYjZgAAgNWIGQAAYDViBgAAWI2YAQAAViNmAACA1YgZAABgNWIGAABYjZgBAABWI2YAAIDViBkAAGA1YgYAAFiNmAEAAFYjZgAAgNWIGQAAYDViBgAAWI2YAQAAViNmAACA1YgZAABgNWIGAABYjZgBAABWI2YAAIDViBkAAGA1YgYAAFiNmAEAAFYjZgAAgNWIGQAAYDViBgAAWI2YAQAAViNmAACA1SIWM/v27dPIkSOVkZGhdu3a6YorrtC0adNUU1MTsm7Lli269dZb1bZtW6WlpWnu3LmRGgkAALRAbSJ1xTt27FBdXZ1eeeUVde/eXVu3btWoUaN08uRJPf/885Ikv9+vwYMHKzc3V4sXL9aXX36pP/3pT0pISNDDDz8cqdEAAEALEmWMMU11Y/PmzdOiRYv01VdfSZIWLVqkp556Sl6vVzExMZKkyZMna+XKldqxY0e91xEIBBQIBIL7Pp9P6enp2r9/v+Lj4yN/EgAAoNH8fr/S0tJUXV0tt9vdqOuK2DMz9fH5fOrUqVNwv7y8XLfddlswZCQpLy9Pc+bM0XfffaeOHTuedR0lJSWaMWPGWcfT0tIiMzQAAIiYY8eO2RMzu3fv1oIFC4IvMUmS1+tVRkZGyLqUlJTgZfXFzJQpU1RcXBzcr66uVteuXVVZWdnoPwyb/FS0l9ozUpw3530p4Lw570vBT6+s/PxJjl+rwTEzefJkzZkz57xrtm/frh49egT3Dx48qPz8fA0fPlyjRo1q+JQ/43K55HK5zjrudrsvqf8JfhIfH895X0I470sL531puVTPu1Wrxn8WqcExM3HiRBUWFp53TWZmZvC/Dx06pIEDB6p///76+9//HrLO4/Goqqoq5NhP+x6Pp6GjAQCAS1CDYyYpKUlJSUkXtfbgwYMaOHCg+vbtq9LS0rPqKycnR0899ZROnz6t6OhoSdKqVauUlZVV70tMAAAAvxSx75k5ePCgBgwYoPT0dD3//PM6evSovF6vvF5vcM0f/vAHxcTEaOTIkdq2bZvefPNN/fWvfw15T8yFuFwuTZs2rd6XnloyzpvzvhRw3pz3pYDzbvx5R+yj2UuWLNFDDz1U72U/v8ktW7aoqKhIn332mRITEzV27FhNmjQpEiMBAIAWqEm/ZwYAACDc+N1MAADAasQMAACwGjEDAACsRswAAACrWRsz+/bt08iRI5WRkaF27drpiiuu0LRp01RTUxOybsuWLbr11lvVtm1bpaWlae7cuQ5NHD6zZs1S//79FRsbq4SEhHrXREVFnbUtX768aQcNs4s578rKSg0ZMkSxsbFKTk7W448/rjNnzjTtoBHWrVu3s+7b2bNnOz1W2C1cuFDdunVT27ZtlZ2drU8//dTpkSJu+vTpZ923P/829ZZi3bp1uuOOO5SamqqoqCitXLky5HJjjKZOnaouXbqoXbt2ys3N1a5du5wZNowudN6FhYVn3f/5+fnODBsmJSUluvHGGxUXF6fk5GQNHTpUO3fuDFlz6tQpFRUVqXPnzurQoYOGDRt21hfqXoi1MbNjxw7V1dXplVde0bZt2/TCCy9o8eLFevLJJ4Nr/H6/Bg8erK5du2rTpk2aN2+epk+fftY3EdumpqZGw4cP1+jRo8+7rrS0VIcPHw5uQ4cObZoBI+RC511bW6shQ4aopqZG69ev19KlS7VkyRJNnTq1iSeNvJkzZ4bct2PHjnV6pLB68803VVxcrGnTpumLL75Qr169lJeXpyNHjjg9WsRde+21IfftJ5984vRIYXfy5En16tVLCxcurPfyuXPn6qWXXtLixYu1ceNGtW/fXnl5eTp16lQTTxpeFzpvScrPzw+5/5ctW9aEE4bf2rVrVVRUpA0bNmjVqlU6ffq0Bg8erJMnTwbXTJgwQe+8847eeustrV27VocOHdLdd9/dsBsyLcjcuXNNRkZGcP/ll182HTt2NIFAIHhs0qRJJisry4nxwq60tNS43e56L5NkVqxY0aTzNJVznfd7771nWrVqZbxeb/DYokWLTHx8fMj/A7br2rWreeGFF5weI6L69etnioqKgvu1tbUmNTXVlJSUODhV5E2bNs306tXL6TGa1C//raqrqzMej8fMmzcveKy6utq4XC6zbNkyByaMjPr+jR4xYoS58847HZmnqRw5csRIMmvXrjXG/HjfRkdHm7feeiu4Zvv27UaSKS8vv+jrtfaZmfr4fL6Q375ZXl6u2267TTExMcFjeXl52rlzp7777jsnRmxSRUVFSkxMVL9+/fTaa6+FfFlhS1ReXq7rrrsu+JvXpR/vb7/fr23btjk4WfjNnj1bnTt3Vu/evTVv3rwW9VJaTU2NNm3apNzc3OCxVq1aKTc3V+Xl5Q5O1jR27dql1NRUZWZm6v7771dlZaXTIzWpvXv3yuv1htz/brdb2dnZl8T9v2bNGiUnJysrK0ujR4/WsWPHnB4prHw+nyQFH6s3bdqk06dPh9zfPXr0UHp6eoPu7wb/bqbmavfu3VqwYIGef/754DGv16uMjIyQdT890Hm93hb9+59mzpyp22+/XbGxsfrwww/16KOP6sSJExo3bpzTo0WM1+sNCRkp9P5uKcaNG6c+ffqoU6dOWr9+vaZMmaLDhw9r/vz5To8WFt98841qa2vrvS937Njh0FRNIzs7W0uWLFFWVpYOHz6sGTNm6NZbb9XWrVsVFxfn9HhN4qe/q/Xd/y3p73F98vPzdffddysjI0N79uzRk08+qYKCApWXl6t169ZOj9dodXV1Gj9+vG6++Wb17NlT0o/3d0xMzFnvg2zo/d3snpmZPHlyvW9e/fn2y3/QDh48qPz8fA0fPlyjRo1yaPLG+TXnfT7PPPOMbr75ZvXu3VuTJk3SE088oXnz5kXwDH6dcJ+3rRry51BcXKwBAwbo+uuv1yOPPKK//OUvWrBggQKBgMNngcYqKCjQ8OHDdf311ysvL0/vvfeeqqur9a9//cvp0dAE7r33Xv3ud7/Tddddp6FDh+rdd9/VZ599pjVr1jg9WlgUFRVp69atEfkwSrN7ZmbixIkqLCw875rMzMzgfx86dEgDBw5U//79z3pjr8fjOesd0T/tezye8AwcJg0974bKzs7Ws88+q0Ag0Kx+mVk4z9vj8Zz1iZfmen//UmP+HLKzs3XmzBnt27dPWVlZEZiuaSUmJqp169b1/t1t7vdjuCUkJOiqq67S7t27nR6lyfx0H1dVValLly7B41VVVbrhhhscmsoZmZmZSkxM1O7duzVo0CCnx2mUMWPG6N1339W6det0+eWXB497PB7V1NSouro65NmZhv59b3Yxk5SUpKSkpItae/DgQQ0cOFB9+/ZVaWmpWrUKfaIpJydHTz31lE6fPq3o6GhJ0qpVq5SVldXsXmJqyHn/GhUVFerYsWOzChkpvOedk5OjWbNm6ciRI0pOTpb04/0dHx+va665Jiy3ESmN+XOoqKhQq1atgudsu5iYGPXt21dlZWXBT+DV1dWprKxMY8aMcXa4JnbixAnt2bNHDzzwgNOjNJmMjAx5PB6VlZUF48Xv92vjxo0X/ARnS3PgwAEdO3YsJOpsY4zR2LFjtWLFCq1Zs+ast3707dtX0dHRKisr07BhwyRJO3fuVGVlpXJychp0Q1Y6cOCA6d69uxk0aJA5cOCAOXz4cHD7SXV1tUlJSTEPPPCA2bp1q1m+fLmJjY01r7zyioOTN97XX39tNm/ebGbMmGE6dOhgNm/ebDZv3myOHz9ujDHm3//+t/nHP/5hvvzyS7Nr1y7z8ssvm9jYWDN16lSHJ2+cC533mTNnTM+ePc3gwYNNRUWF+eCDD0xSUpKZMmWKw5OHz/r1680LL7xgKioqzJ49e8w///lPk5SUZB588EGnRwur5cuXG5fLZZYsWWL+97//mYcfftgkJCSEfFKtJZo4caJZs2aN2bt3r/nPf/5jcnNzTWJiojly5IjTo4XV8ePHg39/JZn58+ebzZs3m6+//toYY8zs2bNNQkKCefvtt82WLVvMnXfeaTIyMswPP/zg8OSNc77zPn78uHnsscdMeXm52bt3r/noo49Mnz59zJVXXmlOnTrl9Oi/2ujRo43b7TZr1qwJeZz+/vvvg2seeeQRk56ebj7++GPz+eefm5ycHJOTk9Og27E2ZkpLS42keref++9//2tuueUW43K5zGWXXWZmz57t0MThM2LEiHrPe/Xq1cYYY95//31zww03mA4dOpj27dubXr16mcWLF5va2lpnB2+kC523Mcbs27fPFBQUmHbt2pnExEQzceJEc/r0aeeGDrNNmzaZ7Oxs43a7Tdu2bc3VV19tnnvuOav/sTuXBQsWmPT0dBMTE2P69etnNmzY4PRIEXfPPfeYLl26mJiYGHPZZZeZe+65x+zevdvpscJu9erV9f5dHjFihDHmx49nP/PMMyYlJcW4XC4zaNAgs3PnTmeHDoPznff3339vBg8ebJKSkkx0dLTp2rWrGTVqlPUBf67H6dLS0uCaH374wTz66KOmY8eOJjY21tx1110hT0xcjKj/f2MAAABWanafZgIAAGgIYgYAAFiNmAEAAFYjZgAAgNWIGQAAYDViBgAAWI2YAQAAViNmAACA1YgZAABgNWIGAABYjZgBAABW+39cpCOHTOFskAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n",
      "Code test passed\n",
      "Go on to the next step\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "xmin = -20\n",
    "xmax = 20\n",
    "ymin = -20\n",
    "ymax = 20\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "plt.axis([xmin,xmax,ymin,ymax]) # window size\n",
    "plt.show()\n",
    "\n",
    "# Only change code above this line\n",
    "import math_code_test_b as test\n",
    "test.step03(In[-1].split('# Only change code above this line')[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "jIHKROStFMcR"
   },
   "source": [
    "# Step 4 - Displaying Axis Lines"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "NhrHvY1YEndp"
   },
   "source": [
    "Notice the code to `plot` a line for the x axis and a line for the y axis. The `'b'` makes the line blue. Run the code, then change each 'b' to 'g' to make the lines green. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "id": "mgWhRLtwFGOd",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n",
      "Code test passed\n",
      "Go on to the next step\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "xmin = -10\n",
    "xmax = 10\n",
    "ymin = -10\n",
    "ymax = 10\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "plt.axis([xmin,xmax,ymin,ymax]) # window size\n",
    "plt.plot([xmin,xmax],[0,0],'g') # blue x axis\n",
    "plt.plot([0,0],[ymin,ymax], 'g') # blue y axis\n",
    "\n",
    "plt.show()\n",
    "\n",
    "# Only change code above this line\n",
    "import math_code_test_b as test\n",
    "test.step04(In[-1].split('# Only change code above this line')[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "wLDO_IRrFw7z"
   },
   "source": [
    "# Step 5 - Plotting a Point"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "iOZ8TJISFw71"
   },
   "source": [
    "Now you will plot a point on the graph. Notice the `'ro'` makes the point a red dot. Run the code, then change the location of the point to (-5,1) and run it again. Keep the window size the same. Notice the difference between plotting a point and plotting a line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "id": "N09NlV3DFw71",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n",
      "Code test passed\n",
      "Go on to the next step\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "xmin = -10\n",
    "xmax = 10\n",
    "ymin = -10\n",
    "ymax = 10\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "plt.axis([xmin,xmax,ymin,ymax]) # window size\n",
    "plt.plot([xmin,xmax],[0,0],'b') # blue x axis\n",
    "plt.plot([0,0],[ymin,ymax], 'b') # blue y axis\n",
    "\n",
    "# Change only the numbers in the following line:\n",
    "plt.plot([-5],[1], 'ro')\n",
    "\n",
    "plt.show()\n",
    "\n",
    "\n",
    "# Only change code above this line\n",
    "import math_code_test_b as test\n",
    "test.step05(In[-1].split('# Only change code above this line')[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ExVB2joZF0rk"
   },
   "source": [
    "# Step 6 - Plotting Several Points"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "G48kO0jcF0rl"
   },
   "source": [
    "You have actually been using arrays to plot each singular point so far. In this step, you will see an array of x values and an array of y values defined before the plot statement. Notice that these two short arrays create one point: (4,2). Add two numbers to each array so that it also plots points (1,1) and (2,5)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "id": "YkRIMNimF0rm",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n",
      "Code test passed\n",
      "Go on to the next step\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# only change the next two lines:\n",
    "x = [4,1,2]\n",
    "y = [2,1,5]\n",
    "\n",
    "# Only change code above this line\n",
    "\n",
    "xmin = -10\n",
    "xmax = 10\n",
    "ymin = -10\n",
    "ymax = 10\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "plt.axis([xmin,xmax,ymin,ymax]) # window size\n",
    "plt.plot([xmin,xmax],[0,0],'b') # blue x axis\n",
    "plt.plot([0,0],[ymin,ymax],'b') # blue y axis\n",
    "\n",
    "plt.plot(x, y, 'ro') # red points\n",
    "plt.show()\n",
    "\n",
    "\n",
    "# Only change code above this line\n",
    "import math_code_test_b as test\n",
    "test.step06(In[-1].split('# Only change code above this line')[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3MqIpFTOF1m9"
   },
   "source": [
    "# Step 7 - Plotting Points and Lines"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "1O1_p4BqF1m-"
   },
   "source": [
    "Notice the subtle difference between plotting points and lines. Each `plot()` statement takes an array of x values, an array of y values, and a third argument to tell what you are plotting. The default plot is a line. The letters `'r'` and `'b'` (and `'g'` and a few others) indicate common colors. The \"o\" in `'ro'` indicates a dot, where `'rs'` would indicate a red square and `'r^'` would indicate a red triangle. Plot a red line and two green squares. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "id": "oMRcOD7hF1m-",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n",
      "Code test passed\n",
      "Go on to the next step\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Use these numbers:\n",
    "linex = [2,4]\n",
    "liney = [1,5]\n",
    "pointx = [1,6]\n",
    "pointy = [6,3]\n",
    "\n",
    "# Keep these lines:\n",
    "xmin = -10\n",
    "xmax = 10\n",
    "ymin = -10\n",
    "ymax = 10\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "plt.axis([xmin,xmax,ymin,ymax]) # window size\n",
    "plt.plot([xmin,xmax],[0,0],'b') # blue x axis\n",
    "plt.plot([0,0],[ymin,ymax], 'b') # blue y axis\n",
    "\n",
    "# Change the next two lines:\n",
    "plt.plot(linex, liney, 'r')\n",
    "plt.plot(pointx, pointy, 'gs')\n",
    "\n",
    "plt.show()\n",
    "\n",
    "\n",
    "# Only change code above this line\n",
    "import math_code_test_b as test\n",
    "test.step07(In[-1].split('# Only change code above this line')[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "NKq_qwCsF3Dj"
   },
   "source": [
    "# Step 8 - Making a Scatterplot Game"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "sBh-rNyOF3Dk"
   },
   "source": [
    "To make the game, you can make a loop that plots a random point and asks the user to input the (x,y) coordinates. Notice the `for` loop that runs three rounds of the game. Run the code, play the game, then you can go on to the next step."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "id": "uR5TFWbLF3Dk",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      "Enter the coordinates of the red point point: \n",
      " 1,2\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      "Enter the coordinates of the red point point: \n",
      " 3,2\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      "Enter the coordinates of the red point point: \n",
      " -8,2\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your score:  3\n",
      "You scored 3 out of 3. Good job!\n",
      "You can go on to the next step\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import random\n",
    "\n",
    "score = 0\n",
    "\n",
    "xmin = -8\n",
    "xmax = 8\n",
    "ymin = -8\n",
    "ymax = 8\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "for i in range(0,3):\n",
    "    xpoint = random.randint(xmin, xmax)\n",
    "    ypoint = random.randint(ymin, ymax)\n",
    "    x = [xpoint]  \n",
    "    y = [ypoint]\n",
    "    plt.axis([xmin,xmax,ymin,ymax]) # window size\n",
    "    plt.plot([xmin,xmax],[0,0],'b') # blue x axis\n",
    "    plt.plot([0,0],[ymin,ymax], 'b') # blue y axis\n",
    "    plt.plot(x, y, 'ro')\n",
    "    print(\" \")\n",
    "    plt.grid() # displays grid lines on graph\n",
    "    plt.show()\n",
    "    guess = input(\"Enter the coordinates of the red point point: \\n\")\n",
    "    guess_array = guess.split(\",\")\n",
    "    xguess = int(guess_array[0])\n",
    "    yguess = int(guess_array[1])\n",
    "    if xguess == xpoint and yguess == ypoint:\n",
    "        score = score + 1\n",
    "    \n",
    "print(\"Your score: \", score) # notice this is not in the loop\n",
    "\n",
    "\n",
    "# Only change code above this line\n",
    "import math_code_test_b as test\n",
    "test.step08(score)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "wvdngkOTF4Hi"
   },
   "source": [
    "# Step 9 - Graphing Linear Equations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "fTzBZAmtF4Hj"
   },
   "source": [
    "Besides graphing points, you can graph <i>linear equations</i> (or <i>functions</i>). The graph will be a straight line, and the equation will not have any exponents. For these graphs, you will import `numpy` and use the `linspace()` function to define the x values. That function takes three arguments: starting number, ending number, and number of steps. Notice the `plot()` function only has two arguments: the x values and a function (y = 2x - 3) for the y values. Run this code, then use the same x values to graph `y = -x + 3`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "id": "xJ0pkcFsF4Hj",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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lsBwR1bJ+bV3x+4xA+DRUQvWwCJN/PIn5uy6isJjTbERE+oDliEgCHvWtsGWqPyZ0bwQA+OHoNQxbGYOb9/MlTkZERCxHRBIxN5Vh7sBW+D64M5SWZjiTpkJQeBT2nM+QOhoRUZ3GckQksZdaOSNyZiA6etghp6AYU9efwrwd51FQVCJ1NCKiOonliEgPNLCzxKYpfpjSszEAYF3sDQxdEYPrd/MkTkZEVPewHBHpCTMTGcL6tUTEuC6oZ2WGC7fUGLA0GrvO3JI6GhFRncJyRKRnXvB2QuTMQHT1skeuphgzfj6N/2w7x2k2IqJawnJEpIdclZbYONkXIS80hSAAG+NSMWT5UVy5kyt1NCIio8dyRKSnTE1k+FffFvhxQlc42JgjKTMHA5dGY9vpNKmjEREZNZYjIj0X2MwRkaGB8GtcH/mFJXh30xm8t+UMHhZymo2IqCawHBEZACeFBdZP8sU7fZpBEIAt8WkYtCwal7JypI5GRGR0WI6IDISJTMA7fZpjwyRfONrKcfl2LgYti8bmkzchiqLU8YiIjAbLEZGB8W/igD9mBiKwmQMKirT4969nMXvzGeRpiqWORkRkFFiOiAyQg40c68Z3xXt9W0AmAFtPp2PgsmgkZqiljkZEZPBYjogMlEwmYPoLTfHLW35wUVjg6p08DFl+FBvjUjnNRkT0HFiOiAxc10b2iJwZiF4tHKEp1uI/284h9JcE5BQUSR2NiMggsRwRGQF7a3P8MLYLwvp5w1QmYNeZWxi4NBrn01VSRyMiMjgsR0RGQiYTMKVnE2ya4ocGdpa4fi8fr30bgx9jr3OajYioCliOiIxMJ896+D00AH1aOqOwRIu5Oy5g+sZTUD3kNBsR0dNgOSIyQnZW5vg+uBM+HNAKZiYCIs9lYsDSKJy5mS11NCIivcdyRGSkBEHAxIBG+HWqP9ztLXHz/kO8vjIGa6KvcZqNiKgSLEdERs7H3Q67ZwSiXxsXFJWIWLD7Iib/GI/s/EKpoxER6SWWI6I6QGlphm9Hd8T8wa1hbiLD/sQs9A+PRvyNB1JHIyLSO5KXo48++giCIJRZvL29K91my5Yt8Pb2hoWFBdq2bYvIyMhaSktkuARBQLCfF7a+7Q/P+lZIz36IEatiserwFWi1nGYjInpE8nIEAK1bt0ZGRoZuiY6OrnBsTEwMRo4ciYkTJ+L06dMYMmQIhgwZgvPnz9diYiLD1aaBErtnBGBAO1cUa0Us/CMJE9edwP08TrMREQF6Uo5MTU3h4uKiWxwcHCocu2TJErzyyit477330LJlSyxYsAAdO3bEsmXLajExkWGztTDD0pEd8L9X28LcVIaDyXcQtCQKx6/dlzoaEZHk9KIcXb58GW5ubmjcuDFGjx6N1NTUCsfGxsaiT58+Zdb17dsXsbGxFW6j0WigVqvLLER1nSAIGOXrgR3Tu6OxozUy1QUY+f0xLD+Ywmk2IqrTJC9Hvr6+WLt2Lfbs2YMVK1bg2rVrCAwMRE5OTrnjMzMz4ezsXGads7MzMjMzK3yMhQsXQqlU6hZ3d/dqPQYiQ9bSVYFdIQF4rUMDlGhFfLE3GWMjjuNurkbqaEREkpC8HPXr1w/Dhg1Du3bt0LdvX0RGRiI7OxubN2+utscICwuDSqXSLTdv3qy2fRMZA2u5Kb4c7oPPX28HCzMZoi7fRdCSKMReuSd1NCKiWid5OfonOzs7NG/eHCkpKeXe7+LigqysrDLrsrKy4OLiUuE+5XI5FApFmYWIyhIEAcM7u2NnSACaOdngdo4Go1cfwzf7L6GE02xEVIfoXTnKzc3FlStX4OrqWu79fn5+OHDgQJl1+/btg5+fX23EIzJ6zZ1tsTMkAMM7N4RWBL7ZfxlvronDbXWB1NGIiGqF5OXoX//6Fw4fPozr168jJiYGr776KkxMTDBy5EgAQHBwMMLCwnTjZ86ciT179uDLL79EUlISPvroI5w8eRIhISFSHQKR0bE0N8Hnr/vgq+E+sDI3QcyVewgKj0LU5TtSRyMiqnGSl6O0tDSMHDkSLVq0wPDhw1G/fn0cO3YMjo6OAIDU1FRkZGToxvv7+2Pjxo347rvv4OPjg19//RXbt29HmzZtpDoEIqP1WseG2BkSAG8XW9zNLUTwD8exeG8yiku0UkcjIqoxglgHv4FSrVZDqVRCpVLx+iOip1BQVIL5uy9iY9zfH7PR1cse4SM7wEVpIXGysvLyABubv3/OzQWsraXNQ0TVq7aevyV/5YiI9J+FmQn+92pbhI/sABu5KY5fv4+g8CgcTL4tdTQiomrHckRET22Qjxt2zQhAazcF7ucVYnzECSz8IxFFnGYjIiPCckREVdLIwRq/TfNHsJ8nAGDV4at447tjSM9+KHEyIqLqwXJERFVmYWaC+YPbYMXojrC1MEX8jQcIWhKF/ReznrwxEZGeYzkiomfWr60rfp8RCJ+GSqgeFmHSjyfxye6LKCzmNBsRGS6WIyJ6Lh71rbBlqj8mdG8EAFgdfQ3DVsXi5v18iZMRET0bliMiem7mpjLMHdgK3wd3htLSDGduZiMoPAp7zmc8eWMiIj3DckRE1ealVs74PTQAHTzskFNQjKnrT2HejvPQFJdIHY2I6KmxHBFRtWpYzwqbp/hhSs/GAIB1sTcwdEUMrt/NkzgZEdHTYTkiompnZiJDWL+WiBjXBfWszHA+XY0BS6Ox++wtqaMRET0RyxER1ZgXvJ0QOTMQXbzqIVdTjJCNp/HfbedQUMRpNiLSXyxHRFSjXJWW+HlyN0x/oQkEAdgQl4ohy4/iyp1cqaMREZWL5YiIapypiQzv9fXGuvFdUd/aHEmZORi4NBrbT6dLHY2I6DEsR0RUa3o0d8QfMwPRrbE98gtL8M6mBLz/61k8LOQ0GxHpD5YjIqpVTgoLbJjUDTN7N4MgAJtO3sTg5dG4nJUjdTQiIgAsR0QkAROZgHdfao4NE33haCvHpaxcDFp2FFtO3pQ6GhERyxERSce/qQMiQwMR0NQBD4tK8N6vZzFrcwLyNMVSRyOiOozliIgk5Wgrx48TuuJfLzeHTAC2nkrHoGXRSMpUSx2NiOooliMikpxMJiDkxWb4eXI3OCvkuHInD4OXHcXPx1MhiqLU8YiojmE5IiK94du4PiJDA9GrhSM0xVqEbT2H0F8SkFNQJHU0IqpDWI6ISK/Ut5Hjh7FdMKefN0xkAnaduYWBS6NxPl0ldTQiqiNYjohI78hkAqb2bILNU7rBTWmB6/fy8dq3Mfgp9jqn2YioxrEcEZHe6uRpj8iZgejT0gmFJVp8uOMCpm88BTWn2YioBrEcEZFes7Myx/fBnfFB/5YwMxEQeS4T/cOjcDYtW+poRGSkWI6ISO8JgoBJgY2xZao/GtazxM37DzF0RQx+iL7GaTYiqnYsR0RkMNq72+H30EC80toFRSUi5u++iCk/xUOVz2k2Iqo+LEdEZFCUlmZYMaYjPh7UGuYmMvx5MQtB4VE4lfpA6mhEZCRYjojI4AiCgLH+Xvhtmj8861shPfshhq+MRUTsFQCcZiOi58NyREQGq21DJXbPCED/dq4o1opYvD8JjkNPQmZRKHU0IjJgLEdEZNBsLcywbGQHfPpqG5ibyGDV9DZcx0chPvW+1NGIyECxHBGRwRMEAaN9PfHzhO4oumcNU0UBxv94DMsPpkCr5TQbEVUNyxERGQ1vFwUyfgxA7gU3lIgivtibjLERx3E3VyN1NCIyICxHRGRUxEJT3NvdHgsGtoOFmQxRl+8iaEkUYq/ckzoaERkIliMiMkICXmvvjh3TA9DUyQa3czQYvfoYluy/jBJOsxHRE7AcEZHRauFii50h3fF6p4bQisDX+y/hzTVxuJ1TIHU0ItJjLEdEZNSszE2xeJgPvhzmA0szE8RcuYegJdGIvnxX6mhEpKckL0cLFy5Ely5dYGtrCycnJwwZMgTJycmVbrN27VoIglBmsbCwqKXERGSIhnZqiF0zAtDC2RZ3czV484c4fPlnMopLtFJHIyI9I3k5Onz4MKZPn45jx45h3759KCoqwssvv4y8vLxKt1MoFMjIyNAtN27cqKXERGSomjrZYEdId4zs6g5RBJb+lYJRq+OQqeI0GxH9H1OpA+zZs6fM7bVr18LJyQnx8fHo0aNHhdsJggAXF5enegyNRgON5v/eyqtWq58tLBEZPAszEyx8rR26Na6P/2w9h+PX7iMoPApfDfdBrxZOUscjIj0g+StH/6RSqQAA9vb2lY7Lzc2Fp6cn3N3dMXjwYFy4cKHCsQsXLoRSqdQt7u7u1ZqZiAzP4PYNsDs0EK1cFbifV4hxESfw2Z4kFHGajajOE0RR1Jv3tWq1WgwaNAjZ2dmIjo6ucFxsbCwuX76Mdu3aQaVSYfHixThy5AguXLiAhg0bPja+vFeO3N3doVKpoFAoauRYiKj25eUBNjZ//5ybC1hbP3mbgqISfPp7In469vfUfCfPelg6sgPc7CxrMCkRPQu1Wg2lUlnjz996VY6mTZuGP/74A9HR0eWWnIoUFRWhZcuWGDlyJBYsWPDE8bX1yyWi2vUs5eiRyHMZeP/Xs8jRFMPOygyLX/dBn1bONROUiJ5JbT1/6820WkhICHbv3o2DBw9WqRgBgJmZGTp06ICUlJQaSkdExi6orSt+Dw1Eu4ZKZOcXYdKPJ/HJ7osoLOY0G1FdI3k5EkURISEh2LZtG/766y80atSoyvsoKSnBuXPn4OrqWgMJiaiu8KhvhS1T/TC+uxcAYHX0NQxbFYub9/OlDUZEtUrycjR9+nSsX78eGzduhK2tLTIzM5GZmYmHDx/qxgQHByMsLEx3e/78+fjzzz9x9epVnDp1CmPGjMGNGzcwadIkKQ6BiIyI3NQE8wa2xqo3O0FhYYozN7PRPzwKe85nSh2NiGqJ5OVoxYoVUKlU6NWrF1xdXXXLpk2bdGNSU1ORkZGhu/3gwQNMnjwZLVu2RFBQENRqNWJiYtCqVSspDoGIjFDf1i6InBmI9u52UBcUY+r6eHy08wI0xSVSRyOiGqZXF2TXFl6QTWScnueC7IoUlWjxxd5kfHfkKgCgbQMllo3qAM/61bBzIqqSOndBNhGRPjIzkeE/QS3xw7jOsLMyw7l0FfqHR2P32VtSRyOiGsJyRET0FF70dkZkaCA6e9ZDrqYYIRtP47/bzqGgiNNsRMaG5YiI6Cm52Vnil7e64e1eTQAAG+JSMWT5UVy5kytxMiKqTixHRERVYGoiw79f8ca6CV1R39ocSZk5GLg0GttPp0sdjYiqCcsREdEz6NncEZEzA9GtsT3yC0vwzqYEvP/rWTws5DQbkaFjOSIiekbOCgtsmNQNob2bQRCATSdvYvDyaFzOypE6GhE9B5YjIqLnYCITMOul5lg/0RcONnJcysrFoGVHseXkTamjEdEzYjkiIqoG3Zs64I+ZgQho6oCHRSV479ezmLU5AXmaYqmjEVEVsRwREVUTR1s51k3oitkvNYdMALaeSsegZdFIylRLHY2IqoDliIioGpnIBMzo3QwbJ3eDs0KOK3fyMHjZUfx8PBV18AsJiAwSyxERUQ3o1rg+IkMD0bO5IzTFWoRtPYeZvyQgl9NsRHqP5YiIqIbUt5EjYlwXvP+KN0xkAnaeuYUB4VE4n66SOhoRVYLliIioBslkAqb1aoJNb3WDq9IC1+/l47UVMfgp9jqn2Yj0FMsREVEt6Oxlj8jQQPT2dkJhsRYf7riA6RtPQV1QJHU0IvoHliMiolpSz9ocq8d2xgf9W8JUJiDyXCYGhEfjbFq21NGIqBSWIyKiWiQIAiYFNsaWqX5oYGeJ1Pv5GLoiBj9EX+M0G5GeYDkiIpJAB496iAwNRN/WzigqETF/90VM+SkeqnxOsxFJjeWIiEgiSiszrBzTCR8NbAVzExn+vJiFoPAonE59IHU0ojqN5YiISEKCIGBc90b4bZo/POytkJ79EMNWxuL7I1eh1XKajUgKLEdERHqgbUMldocGoH87VxRrRXwamYhJP57Eg7xCqaMR1TksR0REekJhYYZlIzvgkyFtYG4qw19JtxEUHoUT1+9LHY2oTmE5IiLSI4IgYEw3T2x72x+NHKyRoSrAG98dw/KDKZxmI6olLEdERHqotZsSu2YEYHB7N5RoRXyxNxnj1p7A3VyN1NGIjB7LERGRnrKRm+KbEe3x2dC2kJvKcOTSHQQticKxq/ekjkZk1FiOiIj0mCAIGNHFAztDAtDUyQa3czQY9f0xLNl/GSWcZiOqESxHREQGoIWLLXaGdMfQjg2hFYGv919C8A9xuJ1TIHU0IqPDckREZCCszE3x5XAfLB7mA0szExxNuYegJdE4mnJX6mhERoXliIjIwLzeqSF2zeiOFs62uJurwZg1cfjqz2QUl2iljkZkFFiOiIgMUFMnW+wI6Y6RXd0hikD4XykYtToOWWpOsxE9L5YjIiIDZWFmgoWvtcOSN9rD2twEx6/dR78lUTiUfFvqaEQGjeWIiMjADW7fALtmBKCVqwL38woxLuIEPtuTxGk2omfEckREZAQaO9pg69v+eLObJwBgxaEreOO7Y7iV/VDiZESGh+WIiMhIWJiZYMGQNlg+qiNs5aY4eeMBgsKjcCAxS+poRAaF5YiIyMj0b+eK30MD0a6hEtn5RZi47iQ+2X0RhcWcZiN6GixHRERGyKO+FbZM9cP47l4AgNXR1zB8VSxu3s+XNhiRAdCLcrR8+XJ4eXnBwsICvr6+OH78eKXjt2zZAm9vb1hYWKBt27aIjIyspaRERIZDbmqCeQNbY9WbnaCwMEXCzWz0D4/C3guZUkcj0muCKIqSfjnPpk2bEBwcjJUrV8LX1xfffPMNtmzZguTkZDg5OT02PiYmBj169MDChQsxYMAAbNy4EZ999hlOnTqFNm3aPNVjqtVqKJVK3LqlgkKhqO5DIiKJ5OUBzs5//5yVBVhbS5tHn9zKzsfsradxNj0bADCmqxdm9/aGuamJtMGIqkCtVsPNTQmVqmafvyUvR76+vujSpQuWLVsGANBqtXB3d8eMGTMwZ86cx8aPGDECeXl52L17t25dt27d0L59e6xcubLcx9BoNNBoNLrbarUa7u7uAFQAWI6IqI6QaWHXIxlK36sAAE2GEnd3dkBxNlskGQo1gJovR5JOqxUWFiI+Ph59+vTRrZPJZOjTpw9iY2PL3SY2NrbMeADo27dvheMBYOHChVAqlbrl72JERFTHaGXIPtQSt7d0RslDM8hdVXAdFw2rFhlSJyPSK6ZSPvjdu3dRUlIC50evg/9/zs7OSEpKKnebzMzMcsdnZlY8hx4WFoZZs2bpbj965ejWLYCzakTGg9NqT8sZGapAvLftNE7ffADHIacwopMH3n+5FeScZiM9plYDbm41/ziSlqPaIpfLIZfLH1tvbc0/nkTGiv99V66ptSW2TO2Gr/ZdwreHrmBTfCrO3srG8lEd0NjRRup4ROUqKamdx5F0Ws3BwQEmJibIyir7AWVZWVlwcXEpdxsXF5cqjSciovKZmsjw71e8sW5CV9S3NkdihhoDl0ZjR0K61NGIJCVpOTI3N0enTp1w4MAB3TqtVosDBw7Az8+v3G38/PzKjAeAffv2VTieiIgq17O5IyJnBqJbY3vkFZZg5i8JmPPbWTwsrKX/TSfSM5J/ztGsWbPw/fffY926dUhMTMS0adOQl5eH8ePHAwCCg4MRFhamGz9z5kzs2bMHX375JZKSkvDRRx/h5MmTCAkJkeoQiIgMnrPCAhsmdUNo72YQBOCXEzcxZPlRpNzOkToaUa2TvByNGDECixcvxty5c9G+fXskJCRgz549uouuU1NTkZHxf++k8Pf3x8aNG/Hdd9/Bx8cHv/76K7Zv3/7Un3FERETlM5EJmPVSc6yf6AsHGzmSs3IwcOlR/BqfJnU0olol+eccSeHRh0DW9OckEFHtyssDbP7/tcS5ubwg+3nczinAu5sScDTlHgBgaMeGWDCkNazM68T7eEhP1dbzt+SvHBERkf5xsrXAjxN8Mful5pAJwG+n0jBo2VEkZ3KajYwfyxEREZXLRCZgRu9m2Di5G5wVcqTczsXg5dHYdCIVdXDSgeoQliMiIqpUt8b1ERkaiJ7NHVFQpMX7v53Du5sSkKspljoaUY1gOSIioieqbyNHxLgueP8Vb5jIBGxPuIVBS6Nx8ZZa6mhE1Y7liIiInopMJmBarybY9FY3uCotcPVuHoZ8exTrj93gNBsZFZYjIiKqks5e9ogMDURvbycUFmvxwfbzCPn5NNQFRVJHI6oWLEdERFRl9azNsXpsZ3zQvyVMZQJ+P5uBgUujcS5NJXU0oufGckRERM9EEARMCmyMLVP90MDOEjfu5WPoihisPXqN02xk0FiOiIjouXTwqIfI0EC83MoZhSVafLTrIqauj4cqn9NsZJhYjoiI6Lkprcyw6s1O+GhgK5ibyLD3Qhb6L41Cws1sqaMRVRnLERERVQtBEDCueyP8Ns0fHvZWSHvwEK+viMHqqKucZiODwnJERETVqm1DJXaHBqB/W1cUa0V88nsiJq07iQd5hVJHI3oqLEdERFTtFBZmWDaqAz4Z0gbmpjIcSLqN/uFRiL9xX+poRE/EckRERDVCEASM6eaJbW/7o5GDNW6pCjB81TGsOHQFWi2n2Uh/sRwREVGNau2mxK4ZARjc3g0lWhGf7UnC+LUncC9XI3U0onKxHBERUY2zkZvimxHtsei1tpCbynD40h0EhUch7uo9qaMRPYbliIiIaoUgCHijqwd2hgSgiaM1stQajPz+GJYeuIwSTrORHmE5IiKiWtXCxRa7ZgRgaMeG0IrAl/suIfiHONzJ4TQb6QeWIyIiqnVW5qb4crgPFg/zgaWZCY6m3EO/JVE4mnJX6mhELEdERCSd1zs1xK4Z3dHC2RZ3czUYsyYOX+27xGk2khTLERERSaqpky22T++ON7q4QxSB8AOXMXr1MWSpC6SORnUUyxEREUnO0twEi4a2w5I32sPa3ATHrt5H0JIoHL50R+poVAexHBERkd4Y3L4Bds0IQEtXBe7lFWLsD8fx+Z4kFJdopY5GdQjLERER6ZXGjjbY9rY/xnTzAAB8e+gK3vjuGG5lP5Q4GdUVLEdERKR3LMxM8MmQtlg2qgNs5KY4eeMBgsKj8FdSltTRqA5gOSIiIr01oJ0bfg8NQNsGSmTnF2HC2pP4X2QiijjNRjWI5YiIiPSaZ31r/DrND+P8vQAA3x25imErY5H2IF/aYGS0WI6IiEjvyU1N8NGg1lg5phMUFqZIuJmNoCVR2HshU+poZIRYjoiIyGC80sYFv4cGwsfdDuqCYkz5KR4f77qAwmJOs1H1YTkiIiKD4m5vhS1T/DA5sBEAIOLodby+Mgap9zjNRtWD5YiIiAyOuakM/+3fCquDO8POygxn01ToHx6FyHMZUkcjI8ByREREBqtPK2f8HhqITp71kKMpxtsbTuHD7edRUFQidTQyYCxHRERk0BrYWeKXt7phas8mAICfjt3Aa9/G4NrdPImTkaFiOSIiIoNnZiLDnH7eWDu+C+ytzXExQ40B4VHYkZAudTQyQCxHRERkNHq1cEJkaCC6NrJHXmEJZv6SgLCtZznNRlUiWTm6fv06Jk6ciEaNGsHS0hJNmjTBvHnzUFhYWOl2vXr1giAIZZapU6fWUmoiItJ3LkoLbJzkixkvNoUgAD8fv4khy48i5Xau1NHIQJhK9cBJSUnQarVYtWoVmjZtivPnz2Py5MnIy8vD4sWLK9128uTJmD9/vu62lZVVTcclIiIDYmoiw+yXW8C3UX28sykBSZk5GLg0Gp8MaYOhnRpKHY/0nCCKoih1iEe++OILrFixAlevXq1wTK9evdC+fXt88803z/w4arUaSqUSKpUKCoXimfdDRPolLw+wsfn759xcwNpa2jykH27nFODdTQk4mnIPAPB6p4aYP7g1rMwle32AnlFtPX/r1TVHKpUK9vb2Txy3YcMGODg4oE2bNggLC0N+fuUf/KXRaKBWq8ssRERUNzjZWuDHCb6Y9VJzyATg1/g0DF52FJeycqSORnpKb8pRSkoKli5diilTplQ6btSoUVi/fj0OHjyIsLAw/PTTTxgzZkyl2yxcuBBKpVK3uLu7V2d0IiLScyYyAaG9m2HDpG5wspXj8u1cDFoWjU0nUqFHEyikJ6p9Wm3OnDn47LPPKh2TmJgIb29v3e309HT07NkTvXr1wurVq6v0eH/99Rd69+6NlJQUNGnSpNwxGo0GGo1Gd1utVsPd3Z3TakRGhtNq9DTu5mowa/MZHLl0BwAwpL0bPnm1LWzknGbTd7U1rVbt5ejOnTu4d+9epWMaN24Mc3NzAMCtW7fQq1cvdOvWDWvXroVMVrUXs/Ly8mBjY4M9e/agb9++T7UNrzkiMk4sR/S0tFoRK49cwZd/XkKJVkRjB2ssG9URrdz4nKDPauv5u9prsqOjIxwdHZ9qbHp6Ol544QV06tQJERERVS5GAJCQkAAAcHV1rfK2RERUN8lkAt7u1RRdvOwR+vNpXL2bhyHfHsXcAa0w2tcDgiBIHZEkJNk1R+np6ejVqxc8PDywePFi3LlzB5mZmcjMzCwzxtvbG8ePHwcAXLlyBQsWLEB8fDyuX7+OnTt3Ijg4GD169EC7du2kOhQiIjJQXbzsERkaiBe9nVBYrMUH288j5OfTyCkokjoaSUiyCdZ9+/YhJSUFKSkpaNiw7GdOPJrpKyoqQnJysu7daObm5ti/fz+++eYb5OXlwd3dHUOHDsUHH3xQ6/mJiMg41LM2x+rgzlgTfQ2f7UnC72czcD5dhWUjO6JtQ6XU8UgCevU5R7WF1xwRGSdec0TP61TqA8zYeBrp2Q9hbiLDf4K8Mdbfi9NseqJOfs4RERGRlDp61ENkaCBebuWMwhItPtp1EdPWn4LqIafZ6hKWIyIiolKUVmZY9WYnzBvYCmYmAvZcyET/8Cgk3MyWOhrVEpYjIiKifxAEAeO7N8Jv0/zhYW+FtAcP8fqKGKyOusoPjawDWI6IiIgq0K6hHXaHBqB/W1cUa0V88nsiJv94Etn5hVJHoxrEckRERFQJhYUZlo3qgAVD2sDcVIb9ibcRtCQK8TfuSx2NagjLERER0RMIgoA3u3li29v+aORgjVuqAgxfdQwrD1+BVstpNmPDckRERPSUWrspsWtGAAb5uKFEK2LRH0mYsO4E7uVqnrwxGQyWIyIioiqwkZtiyRvtsei1tpCbynAo+Q6CwqMQd7Xy7xUlw8FyREREVEWCIOCNrh7YEdIdTRytkaXWYOT3x7Dsr8ucZjMCLEdERETPyNtFgZ0hAXitYwNoRWDxn5cQ/MNx3MnhNJshYzkiIiJ6DtZyU3w1vD2+eL0dLM1MEJ1yF0HhUYhJuSt1NHpGLEdERETVYFhnd+wM6Y7mzja4k6PB6DVx+HrfJZRwms3gsBwRERFVk2bOttgxPQAjOrtDFIElBy5j9OpjuK0ukDoaVQHLERERUTWyNDfBZ6+3wzcj2sPK3ATHrt5HvyVROHLpjtTR6CmxHBEREdWAIR0aYPeMALR0VeBeXiHGRhzHF3uTUFyilToaPQHLERERUQ1p7GiDbW/7Y7SvB0QRWH7wCkZ9H4cM1UOpo1ElWI6IiIhqkIWZCT59tS2WjeoAG7kpjl+/j6AlUTiYdFvqaFQBliMiIqJaMKCdG3bPCECbBgo8yC/C+LUnsDAyEUWcZtM7LEdERES1xMvBGr9N88c4fy8AwKojVzFiVSzSHuRLG4zKYDkiIiKqRXJTE3w0qDVWjukIWwtTnErNRv/waPx5IVPqaPT/sRwRERFJ4JU2rogMDYSPux1UD4vw1k/xmL/rIgqLOc0mNZYjIiIiibjbW2HLFD9MCmgEAPjh6DUMWxmDm/c5zSYlliMiIiIJmZvK8MGAVlgd3BlKSzOcSVMhKDwKf5zLkDpancVyREREpAf6tHJG5MxAdPKsh5yCYkzbcApzd5xHQVGJ1NHqHJYjIiIiPdHAzhK/vNUNU3s2AQD8GHsDQ1fE4PrdPImT1S0sR0RERHrEzESGOf28ETG+C+ytzXHhlhoDlkZj55lbUkerM1iOiIiI9NALLZwQGRqIrl72yNUUI/Tn0wjbeo7TbLWA5YiIiEhPuSgtsHGyL2a82BSCAPx8PBVDlh/FlTu5UkczaixHREREeszURIbZL7fAjxO6wsHGHEmZORi4NBpbT6VJHc1osRwREREZgMBmjoicGQj/JvWRX1iCWZvP4L0tZ5BfWCx1NKPDckRERGQgnGwt8NNEX7zbpzlkArAlPg2Dlx3FpawcqaMZFZYjIiIiA2IiEzCzTzNsmNQNTrZyXL6di0HLorH55E2Ioih1PKPAckRERGSA/JrUR+TMQAQ2c0BBkRb//vUsZm0+gzwNp9meF8sRERGRgXKwkWPd+K54r28LmMgEbDudjoHLopGYoZY6mkFjOSIiIjJgMpmA6S80xS9vdYOLwgJX7+Rh8PKj2BiXymm2ZyRpOfLy8oIgCGWWRYsWVbpNQUEBpk+fjvr168PGxgZDhw5FVlZWLSUmIiLST1287BE5MxAvejuhsFiL/2w7h9BfEpBTUCR1NIMj+StH8+fPR0ZGhm6ZMWNGpePfffdd7Nq1C1u2bMHhw4dx69YtvPbaa7WUloiISH/ZW5tjdXBn/CfIG6YyAbvO3MLApdE4n66SOppBkbwc2drawsXFRbdYW1tXOFalUmHNmjX46quv8OKLL6JTp06IiIhATEwMjh07VoupiYiI9JNMJuCtHk2weaofGthZ4vq9fLz2bQx+jL3OabanJHk5WrRoEerXr48OHTrgiy++QHFxxVfZx8fHo6ioCH369NGt8/b2hoeHB2JjYyvcTqPRQK1Wl1mIiIiMWUePeogMDcRLrZxRWKLF3B0X8PaGU1A95DTbk0hajkJDQ/HLL7/g4MGDmDJlCv73v//h3//+d4XjMzMzYW5uDjs7uzLrnZ2dkZmZWeF2CxcuhFKp1C3u7u7VdQhERER6S2llhu/e7IS5A1rBzETAH+czMWBpFM7czJY6ml6r9nI0Z86cxy6y/ueSlJQEAJg1axZ69eqFdu3aYerUqfjyyy+xdOlSaDSaas0UFhYGlUqlW27evFmt+yciItJXgiBgQkAj/DbNHx72Vrh5/yFeXxmDNdHXOM1WAdPq3uHs2bMxbty4Ssc0bty43PW+vr4oLi7G9evX0aJFi8fud3FxQWFhIbKzs8u8epSVlQUXF5cKH08ul0Mulz9VfiIiImPUrqEddocGYM5vZxF5LhMLdl9E7JV7WDysHeyszKWOp1eqvRw5OjrC0dHxmbZNSEiATCaDk5NTufd36tQJZmZmOHDgAIYOHQoASE5ORmpqKvz8/J45MxERUV2gsDDD8lEdsT4uFQt2X8T+xCz0D49G+MgO6ORZT+p4ekOya45iY2PxzTff4MyZM7h69So2bNiAd999F2PGjEG9en+foPT0dHh7e+P48eMAAKVSiYkTJ2LWrFk4ePAg4uPjMX78ePj5+aFbt25SHQoREZHBEAQBb3bzxLa3/dHIwRrp2Q8xYlUsVh2+Aq2W02yAhOVILpfjl19+Qc+ePdG6dWt8+umnePfdd/Hdd9/pxhQVFSE5ORn5+fm6dV9//TUGDBiAoUOHokePHnBxccHWrVulOAQiIiKD1dpNiV0zAjDIxw3FWhEL/0jCxHUncD+vUOpokhPEOng1llqthlKphEqlgkKhkDoOEVWTvDzAxubvn3NzgUo+No2I/j9RFPHLiZv4aOcFaIq1cFFYIHxkB3RtZC91tMfU1vO35J9zRERERNIRBAEju3pgR0h3NHG0Rqa6ACO/P4blB1Pq7DQbyxERERHB20WBnSEBeK1jA5RoRXyxNxljI47jbm71fryOIWA5IiIiIgCAtdwUXw1vjy9ebwdLMxNEXb6LfkuiEHPlrtTRahXLEREREZUxrLM7doZ0R3NnG9zJ0WDM6jh8s/8SSurINBvLERERET2mmbMtdkwPwIjO7tCKwDf7L2PM6jjcVhdIHa3GsRwRERFRuSzNTfDZ6+3wzYj2sDI3QezVewgKj0LU5TtSR6tRLEdERERUqSEdGmDXjAB4u9jibm4hgn84jsV7k1FcopU6Wo1gOSIiIqInauJog+3Tu2O0rwdEEVh2MAWjvo9Dhuqh1NGqHcsRERERPRULMxN8+mpbLB3ZATZyUxy/fh9BS6JwMOm21NGqFcsRERERVclAHzfsnhGANg0UeJBfhPFrT2BhZCKKjGSajeWIiIiIqszLwRq/TfPHOH8vAMCqI1cxYlUs0rMNf5qN5YiIiIieidzUBB8Nao2VYzrC1sIUp1KzsSMhXepYz81U6gBERERk2F5p44rWbkpEHL2OKT2aSB3nubEcERER0XNzt7fC3IGtpI5RLTitRkRERFQKyxERERFRKSxHRERERKWwHBERERGVwnJEREREVArLEREREVEpLEdEREREpbAcEREREZXCckRERERUCssRERERUSksR0RERESlsBwRERERlcJyRERERFQKyxERERFRKSxHRERERKWwHBERERGVwnJEREREVArLEREREVEpLEdEREREpbAcEREREZXCckRERERUimTl6NChQxAEodzlxIkTFW7Xq1evx8ZPnTq1FpMTERGRMTOV6oH9/f2RkZFRZt2HH36IAwcOoHPnzpVuO3nyZMyfP19328rKqkYyEhERUd0jWTkyNzeHi4uL7nZRURF27NiBGTNmQBCESre1srIqsy0RERFRddGba4527tyJe/fuYfz48U8cu2HDBjg4OKBNmzYICwtDfn5+peM1Gg3UanWZhYiIiKg8kr1y9E9r1qxB37590bBhw0rHjRo1Cp6ennBzc8PZs2fx/vvvIzk5GVu3bq1wm4ULF+Ljjz+u7shERERkhARRFMXq3OGcOXPw2WefVTomMTER3t7euttpaWnw9PTE5s2bMXTo0Co93l9//YXevXsjJSUFTZo0KXeMRqOBRqPR3Var1XB3d4dKpYJCoajS4xGR/srLA2xs/v45NxewtpY2DxFVL7VaDaVSWePP39X+ytHs2bMxbty4Ssc0bty4zO2IiAjUr18fgwYNqvLj+fr6AkCl5Ugul0Mul1d530RERFT3VHs5cnR0hKOj41OPF0URERERCA4OhpmZWZUfLyEhAQDg6upa5W2JiIiI/knyC7L/+usvXLt2DZMmTXrsvvT0dHh7e+P48eMAgCtXrmDBggWIj4/H9evXsXPnTgQHB6NHjx5o165dbUcnIiIiIyT5Bdlr1qyBv79/mWuQHikqKkJycrLu3Wjm5ubYv38/vvnmG+Tl5cHd3R1Dhw7FBx98UNuxiYiIyEhV+wXZhqC2LugiotrFC7KJjFttPX9LPq1GREREpE9YjoiIiIhKYTkiIiIiKoXliIiIiKgUliMiIiKiUliOiIiIiEphOSIiIiIqheWIiIiIqBSWIyIiIqJSWI6IiIiISmE5IiIiIiqF5YiIiIioFJYjIiIiolJYjoiIiIhKYTkiIiIiKoXliIiIiKgUliMiIiKiUliOiIiIiEphOSIiIiIqheWIiIiIqBSWIyIiIqJSWI6IiIiISmE5IiIiIiqF5YiIiIioFJYjIiIiolJYjoiIiIhKYTkiIiIiKoXliIiIiKgUliMiIiKiUliOiIiIiEphOSIiIiIqheWIiIiIqBSWIyIiIqJSWI6IiIiISmE5IiIiIiqF5YiIiIiolBorR59++in8/f1hZWUFOzu7csekpqaif//+sLKygpOTE9577z0UFxdXut/79+9j9OjRUCgUsLOzw8SJE5Gbm1sDR0BERER1UY2Vo8LCQgwbNgzTpk0r9/6SkhL0798fhYWFiImJwbp167B27VrMnTu30v2OHj0aFy5cwL59+7B7924cOXIEb731Vk0cAhEREdVBgiiKYk0+wNq1a/HOO+8gOzu7zPo//vgDAwYMwK1bt+Ds7AwAWLlyJd5//33cuXMH5ubmj+0rMTERrVq1wokTJ9C5c2cAwJ49exAUFIS0tDS4ubmVm0Gj0UCj0ehuq1QqeHh44ObNm1AoFNV0pEQktbw84NGfgVu3AGtrafMQUfVSq9Vwd3dHdnY2lEplzT2QWMMiIiJEpVL52PoPP/xQ9PHxKbPu6tWrIgDx1KlT5e5rzZo1op2dXZl1RUVFoomJibh169YKM8ybN08EwIULFy5cuHAxguXKlStV7iNVYQqJZGZm6l4xeuTR7czMzAq3cXJyKrPO1NQU9vb2FW4DAGFhYZg1a5budnZ2Njw9PZGamlqzzVPPPGrcde0VMx43j7su4HHzuOuCRzM/9vb2Nfo4VSpHc+bMwWeffVbpmMTERHh7ez9XqOoml8shl8sfW69UKuvUP6pHFAoFj7sO4XHXLTzuuqWuHrdMVrNvtq9SOZo9ezbGjRtX6ZjGjRs/1b5cXFxw/PjxMuuysrJ091W0ze3bt8usKy4uxv379yvchoiIiKgqqlSOHB0d4ejoWC0P7Ofnh08//RS3b9/WTZXt27cPCoUCrVq1qnCb7OxsxMfHo1OnTgCAv/76C1qtFr6+vtWSi4iIiOq2GntdKjU1FQkJCUhNTUVJSQkSEhKQkJCg+0yil19+Ga1atcKbb76JM2fOYO/evfjggw8wffp03RTY8ePH4e3tjfT0dABAy5Yt8corr2Dy5Mk4fvw4jh49ipCQELzxxhsVvlOtPHK5HPPmzSt3qs2Y8bh53HUBj5vHXRfwuGv2uGvsrfzjxo3DunXrHlt/8OBB9OrVCwBw48YNTJs2DYcOHYK1tTXGjh2LRYsWwdT07xe0Dh06hBdeeAHXrl2Dl5cXgL8/BDIkJAS7du2CTCbD0KFDER4eDhsbm5o4DCIiIqpjavxzjoiIiIgMCb9bjYiIiKgUliMiIiKiUliOiIiIiEphOSIiIiIqxSjL0aeffgp/f39YWVnBzs6u3DGpqano378/rKys4OTkhPfeew/FxcWV7vf+/fsYPXo0FAoF7OzsMHHiRN1HE+ijQ4cOQRCEcpcTJ05UuF2vXr0eGz916tRaTP78vLy8HjuGRYsWVbpNQUEBpk+fjvr168PGxgZDhw7VfTCpIbh+/TomTpyIRo0awdLSEk2aNMG8efNQWFhY6XaGeL6XL18OLy8vWFhYwNfX97EPlP2nLVu2wNvbGxYWFmjbti0iIyNrKWn1WLhwIbp06QJbW1s4OTlhyJAhSE5OrnSbtWvXPnZeLSwsailx9fjoo48eO4YnfQODoZ9roPy/X4IgYPr06eWON9RzfeTIEQwcOBBubm4QBAHbt28vc78oipg7dy5cXV1haWmJPn364PLly0/cb1X/PpTHKMtRYWEhhg0bhmnTppV7f0lJCfr374/CwkLExMRg3bp1WLt2LebOnVvpfkePHo0LFy5g37592L17N44cOYK33nqrJg6hWvj7+yMjI6PMMmnSJDRq1AidO3eudNvJkyeX2e7zzz+vpdTVZ/78+WWOYcaMGZWOf/fdd7Fr1y5s2bIFhw8fxq1bt/Daa6/VUtrnl5SUBK1Wi1WrVuHChQv4+uuvsXLlSvznP/954raGdL43bdqEWbNmYd68eTh16hR8fHzQt2/fxz49/5GYmBiMHDkSEydOxOnTpzFkyBAMGTIE58+fr+Xkz+7w4cOYPn06jh07hn379qGoqAgvv/wy8vLyKt1OoVCUOa83btyopcTVp3Xr1mWOITo6usKxxnCuAeDEiRNljnnfvn0AgGHDhlW4jSGe67y8PPj4+GD58uXl3v/5558jPDwcK1euRFxcHKytrdG3b18UFBRUuM+q/n2oUI1+ra3EIiIiRKVS+dj6yMhIUSaTiZmZmbp1K1asEBUKhajRaMrd18WLF0UA4okTJ3Tr/vjjD1EQBDE9Pb3as9eEwsJC0dHRUZw/f36l43r27CnOnDmzdkLVEE9PT/Hrr79+6vHZ2dmimZmZuGXLFt26xMREEYAYGxtbAwlrx+effy42atSo0jGGdr67du0qTp8+XXe7pKREdHNzExcuXFju+OHDh4v9+/cvs87X11ecMmVKjeasSbdv3xYBiIcPH65wTEV//wzJvHnzRB8fn6ceb4znWhRFcebMmWKTJk1ErVZb7v3GcK4BiNu2bdPd1mq1oouLi/jFF1/o1mVnZ4tyuVz8+eefK9xPVf8+VMQoXzl6ktjYWLRt2xbOzs66dX379oVarcaFCxcq3MbOzq7MKy59+vSBTCZDXFxcjWeuDjt37sS9e/cwfvz4J47dsGEDHBwc0KZNG4SFhSE/P78WElavRYsWoX79+ujQoQO++OKLSqdN4+PjUVRUhD59+ujWeXt7w8PDA7GxsbURt0aoVKqn+vZqQznfhYWFiI+PL3OeZDIZ+vTpU+F5io2NLTMe+Pu/d0M/rwCeeG5zc3Ph6ekJd3d3DB48uMK/b/rs8uXLcHNzQ+PGjTF69GikpqZWONYYz3VhYSHWr1+PCRMmQBCECscZw7ku7dq1a8jMzCxzPpVKJXx9fSs8n8/y96EiVfpuNWORmZlZphgB0N3OzMyscJtH3wH3iKmpKezt7SvcRt+sWbMGffv2RcOGDSsdN2rUKHh6esLNzQ1nz57F+++/j+TkZGzdurWWkj6/0NBQdOzYEfb29oiJiUFYWBgyMjLw1VdflTs+MzMT5ubmj12j5uzsbDDn959SUlKwdOlSLF68uNJxhnS+7969i5KSknL/+01KSip3m4r+ezfU86rVavHOO++ge/fuaNOmTYXjWrRogR9++AHt2rWDSqXC4sWL4e/vjwsXLjzxb4C+8PX1xdq1a9GiRQtkZGTg448/RmBgIM6fPw9bW9vHxhvbuQaA7du3Izs7u9IvfTeGc/1Pj85ZVc7ns/x9qIjBlKM5c+bgs88+q3RMYmLiEy/WMwbP8rtIS0vD3r17sXnz5ifuv/R1VG3btoWrqyt69+6NK1euoEmTJs8e/DlV5bhnzZqlW9euXTuYm5tjypQpWLhwocF9F9GznO/09HS88sorGDZsGCZPnlzptvp6vql806dPx/nz5yu99gb4+4u6/fz8dLf9/f3RsmVLrFq1CgsWLKjpmNWiX79+up/btWsHX19feHp6YvPmzZg4caKEyWrPmjVr0K9fv0q/P9QYzrW+MZhyNHv27EqbMwA0btz4qfbl4uLy2NXrj96V5OLiUuE2/7ygq7i4GPfv369wm5ryLL+LiIgI1K9fH4MGDary4/n6+gL4+5UIKZ8sn+ffgK+vL4qLi3H9+nW0aNHisftdXFxQWFiI7OzsMq8eZWVl1fr5/aeqHvetW7fwwgsvwN/fH999912VH09fznd5HBwcYGJi8ti7CCs7Ty4uLlUar89CQkJ0bwap6isCZmZm6NChA1JSUmooXc2zs7ND8+bNKzwGYzrXwN/fP7p///4qv4prDOf60TnLysqCq6urbn1WVhbat29f7jbP8vehQlW6QsnAPOmC7KysLN26VatWiQqFQiwoKCh3X48uyD558qRu3d69ew3igmytVis2atRInD179jNtHx0dLQIQz5w5U83Jas/69etFmUwm3r9/v9z7H12Q/euvv+rWJSUlGdwF2WlpaWKzZs3EN954QywuLn6mfej7+e7atasYEhKiu11SUiI2aNCg0guyBwwYUGadn5+fQV2kq9VqxenTp4tubm7ipUuXnmkfxcXFYosWLcR33323mtPVnpycHLFevXrikiVLyr3fGM51afPmzRNdXFzEoqKiKm1niOcaFVyQvXjxYt06lUr1VBdkV+XvQ4V5qjTaQNy4cUM8ffq0+PHHH4s2Njbi6dOnxdOnT4s5OTmiKP79D6dNmzbiyy+/LCYkJIh79uwRHR0dxbCwMN0+4uLixBYtWohpaWm6da+88orYoUMHMS4uToyOjhabNWsmjhw5staPr6r2798vAhATExMfuy8tLU1s0aKFGBcXJ4qiKKakpIjz588XT548KV67dk3csWOH2LhxY7FHjx61HfuZxcTEiF9//bWYkJAgXrlyRVy/fr3o6OgoBgcH68b887hFURSnTp0qenh4iH/99Zd48uRJ0c/PT/Tz85PiEJ5JWlqa2LRpU7F3795iWlqamJGRoVtKjzH08/3LL7+IcrlcXLt2rXjx4kXxrbfeEu3s7HTvPn3zzTfFOXPm6MYfPXpUNDU1FRcvXiwmJiaK8+bNE83MzMRz585JdQhVNm3aNFGpVIqHDh0qc17z8/N1Y/553B9//LG4d+9e8cqVK2J8fLz4xhtviBYWFuKFCxekOIRnMnv2bPHQoUPitWvXxKNHj4p9+vQRHRwcxNu3b4uiaJzn+pGSkhLRw8NDfP/99x+7z1jOdU5Oju75GYD41VdfiadPnxZv3LghiqIoLlq0SLSzsxN37Nghnj17Vhw8eLDYqFEj8eHDh7p9vPjii+LSpUt1t5/09+FpGWU5Gjt2rAjgseXgwYO6MdevXxf79esnWlpaig4ODuLs2bPLtPODBw+KAMRr167p1t27d08cOXKkaGNjIyoUCnH8+PG6wqXPRo4cKfr7+5d737Vr18r8blJTU8UePXqI9vb2olwuF5s2bSq+9957okqlqsXEzyc+Pl709fUVlUqlaGFhIbZs2VL83//+V+ZVwX8etyiK4sOHD8W3335brFevnmhlZSW++uqrZYqFvouIiCj3333pF4iN5XwvXbpU9PDwEM3NzcWuXbuKx44d093Xs2dPcezYsWXGb968WWzevLlobm4utm7dWvz9999rOfHzqei8RkRE6Mb887jfeecd3e/I2dlZDAoKEk+dOlX74Z/DiBEjRFdXV9Hc3Fxs0KCBOGLECDElJUV3vzGe60f27t0rAhCTk5Mfu89YzvWj59l/Lo+OTavVih9++KHo7OwsyuVysXfv3o/9Pjw9PcV58+aVWVfZ34enJYiiKFZtIo6IiIjIeNXJzzkiIiIiqgjLEREREVEpLEdEREREpbAcEREREZXCckRERERUCssRERERUSksR0RERESlsBwRERERlcJyRERERFQKyxERERFRKSxHRERERKX8P42tWicBlgLkAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n",
      "Code test passed\n",
      "Go on to the next step\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "xmin = -10\n",
    "xmax = 10\n",
    "ymin = -10\n",
    "ymax = 10\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "plt.axis([xmin,xmax,ymin,ymax]) # window size\n",
    "plt.plot([xmin,xmax],[0,0],'b') # blue x axis\n",
    "plt.plot([0,0],[ymin,ymax], 'b') # blue y axis\n",
    "\n",
    "x = np.linspace(-9,9,36) \n",
    "\n",
    "# Only change the next line to graph y = -x + 3\n",
    "plt.plot(x, -x + 3)\n",
    "\n",
    "\n",
    "\n",
    "plt.show()\n",
    "\n",
    "\n",
    "# Only change code above this line\n",
    "import math_code_test_b as test\n",
    "test.step09(In[-1].split('# Only change code above this line')[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Q19Wm90DF5zf"
   },
   "source": [
    "# Step 10 - Creating Interactive Graphs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "JNEjD9DxF5zh"
   },
   "source": [
    "Like the previous graphs, you will graph a line. This time, you will create two sliders to change the <i>slope</i> and the <i>y intecept</i>. Notice the additional imports and other changes: You define a function with two arguments. All of the graphing happens within that `f(m,b)` function. The `interactive()` function calls your defined function and sets the boundaries for the sliders. Run this code then adjust the sliders and notice how they affect the graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "id": "9lh41CENF5zh",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Code test Passed\n",
      "Go on to the next step\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "5e07e7fd667746c8a60c7e59efd10f4b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=0, description='m', max=9, min=-9), IntSlider(value=0, description='b', …"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from ipywidgets import interactive\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# Define the graphing function\n",
    "def f(m, b):\n",
    "    xmin = -10\n",
    "    xmax = 10\n",
    "    ymin = -10\n",
    "    ymax = 10\n",
    "    plt.axis([xmin,xmax,ymin,ymax]) # window size\n",
    "    plt.plot([xmin,xmax],[0,0],'black') # black x axis\n",
    "    plt.plot([0,0],[ymin,ymax], 'black') # black y axis\n",
    "    plt.title('y = mx + b')\n",
    "    x = np.linspace(-10, 10, 1000)\n",
    "    plt.plot(x, m*x+b)\n",
    "    plt.show()\n",
    "\n",
    "# Set up the sliders\n",
    "interactive_plot = interactive(f, m=(-9, 9), b=(-9, 9))\n",
    "interactive_plot\n",
    "\n",
    "\n",
    "# Just run this code and use the sliders\n",
    "import math_code_test_b as test\n",
    "test.step01()\n",
    "interactive_plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "YSY2k7S3F6d7"
   },
   "source": [
    "# Step 11 - Graphing Systems"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "8MG28-VPF6d8"
   },
   "source": [
    "When you graph two equations on the same coordinate plane, they are a <i>system of equations</i>. Notice how the `points` variable defines the number of points and the `linspace()` function uses that variable. Run this code to see the graph, then change `y2` so that it graphs y = -x - 3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "id": "wYHGm-PAF6d9",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6htmRRFyKylFhC6ltPw7ppn6AAasnwmf3QsoJs5OJiAAw749jLNtzEk93C2/2aoynu34ViFxMPxGO4FkK7n0XekwDL384sgam3A6xy8xOJiIlXEJyBi99bx+nPdWuNnXCSpucSMT1qBw5UsOe9jFbWENIPwMze8Cyl8CaY3YyESmBDMMgZu52UjJyaFQpkCEtq5sdScQlqRw5WnBNGLgMbnnMvrzmbfsnayfHm5tLREqc2ZvjWbHvFF7ubkzu1QgPjdNE8qSfDGfw9IHOb0KvGeAdAEd/t5/Ntm+x2clEpIQ4nnSBcT/sBmBE+9rUCtU4TSQ/KkfOVP8+GLIawpvAhXPw9QOw5D+Qk2V2MhEpxgzDYPTcHZzPzKFJ5SAGtdA4TeRKVI6crWw1eHQJRD9uX173PkzvBOeOmJtLRIqtbzceZfWfp/DycGNSz0a4u1nMjiTi0lSOzODhDZ0mwANfgk8gHNsEU1vAnoVmJxORYib+XDqv/rgHgGc71KFmeX+TE4m4PpUjM9XtAkPXQMWbISMZvu0DPz0HOZlmJxORYsAwDEZ/t4PUzBxurlKGAbdXMzuSSJGgcmS2oMrw6GJo/oR9ef0UmNYezh40N5eIFHlfbYhjTexpfDzdmNgzSuM0kWukcuQK3D2h/avw0CwoVRZObIWprWDXPLOTiUgRdfRsOq/ljtMiqR6icZrItVI5ciW1O9jHbBG3QWYKzO4PC0dAdobZyUSkCLHZDJ6ds530LCu3Vi1L/+ZVzY4kUqSoHLmawIrQ/0e4Y4R9edM0mNYOzhwwN5eIFBkz1x9h3cEzlPJ0Z1KvKNw0ThMpEJUjV+TuAe3GwsPfgW8wJOyAqS1hxxyzk4mIi4s7k874RXsBGN0pkirl/ExOJFL0mF6OXnrpJSwWyyWXyMjIK24ze/ZsIiMj8fHxoWHDhixatMhJaZ2sZjv7mK1qC8hKhe8GwvdPQPYFs5OJiAuy2QyembONC9lWbqtelkduq2J2JJEiyfRyBFC/fn1OnDiRe1mzZk2+665du5bevXszcOBA/vjjD7p160a3bt3YuXOnExM7UUAF6LsAWj0HWGDL5/DxnXBqn9nJRMTFfLbuMBsOncXXy51JPRtpnCZynVyiHHl4eBAWFpZ7CQ4Oznfd//73v3Ts2JFRo0ZRt25dxo0bx0033cT777/vxMRO5uYObZ6HvvPBrzyc3A0ftYatX5udTERcxKHTabyx2D5Oe/7uukSU9TU5kUjR5RLlaP/+/YSHh1O9enX69OlDXFxcvuuuW7eOdu3aXXJdhw4dWLduXb7bZGZmkpKScsmlSKreGh7/zf7f7HSYPxTm/wuy0sxOJiImstoMRs3eRka2jdtrlqNPdGWzI4kUaaaXo+joaGbMmMHixYv58MMPOXToEC1atOD8+fN5rp+QkEBoaOgl14WGhpKQkJDvY4wfP57AwMDcS0RERKHug1P5l4eH50KbF8DiBlu/hI/aQOJus5OJiEmm/3aITUfO4eflzhs9orBYNE4TuRGml6NOnTrRq1cvoqKi6NChA4sWLSIpKYlZs2YV2mPExMSQnJycezl69Gih3bcp3Nyh1SjotxBKV4DT++zHIW35HAzD7HQi4kQHTqUyaYn9GMQXutSjUhmN00RulOnl6J+CgoKoXbs2sbGxed4eFhZGYmLiJdclJiYSFhaW7316e3sTEBBwyaVYqHq7/Wy2mu0g54L9TLa5gyEz73fdRKR4+Xuclpljo0WtYB68pQi/Ky7iQlyuHKWmpnLgwAEqVKiQ5+3NmjXjl19+ueS6pUuX0qxZM2fEcz1+wfDQbGj3EljcYccs+8HaCTvMTiYiDjZtzUG2xCVR2ttD4zSRQmR6OXrmmWdYtWoVhw8fZu3atdx33324u7vTu3dvAPr27UtMTEzu+k8++SSLFy/mzTffZO/evbz00kts2rSJ4cOHm7UL5nNzgzuehgE/QUAlOBMLH7eFjdM0ZhMppmJPnmfyz38C8GKXeoQHlTI5kUjxYXo5io+Pp3fv3tSpU4f777+fcuXK8fvvvxMSEgJAXFwcJ06cyF2/efPmfPXVV3z00Uc0atSIOXPmMH/+fBo0aGDWLriOytEw9Feo3QmsmfDjCJgzADKSzU4mIoUox2pj5OztZOXYaF0nhF43VzI7kkixYjGMkvfWQkpKCoGBgSQnJxef448uZhiw7gNYNhZsOVCmGvSaDuFNzE4m4lBpaeD/15fPp6aCXzH95oz/WxnLxMX7KO3jwdKnWxEW6GN2JBGncNbvb9PfORIHsFig+XB4dAkEVoZzh2Bae1g/VWM2kSLuz8TzvLN0PwBj76mvYiTiACpHxVmlm2HoaojsAtYs+OlZ+PZhuHDO7GQich2yrTZGztpGltVG28jy9LipotmRRIollaPirlQZeGAmdJoI7l6wdyFMbQnxm8xOJiIFNHXVAXYcSyawlCevd2+os9NEHETlqCSwWCB6CAz8GcpUhaQ4+LQDrH1fYzaRImLPiRT++4t9nPbyvfUJDdA4TcRRVI5KkvAmMGQ11L/PfqD2z/+Brx+E9LNmJxORK8i22nhm9jayrQbt64XStXG42ZFEijWVo5LGJxB6TofOb4G7N/y5GKa0gLj1ZicTkXz834oD7DqeQpCvJ6/e10DjNBEHUzkqiSwWuGUgPLYMytaAlHiY3gnWvA02m9npROQiu44n895y+zjtla4NKF9a4zQRR1M5KskqRMGQVdCwFxhWWPYSfNUL0k6bnUxEgKwc+9lpOTaDTg3CuCcq769VEpHCpXJU0nmXhu4fw73vgYcPxC6DKXfA4d/MTiZS4r2/fD97E85T1s+Lcd00ThNxFpUjsY/ZbuoLg1ZAcG04fwI+6wKrJoHNanY6kRJp57FkPlh5AIBxXRsQ7O9tciKRkkPlSP4ntB4MXgmNHgLDBitehS/ug9STZicTKVEyc6yMnLUNq82gc1QFOmucJuJUKkdyKS8/uO9D6PYhePrCoVXw4e1wcKXZyURKjHd/2c++xPME+3sxrqu+VFvE2VSOJG+NH7KP2ULqQtpJ+LwbrHhdYzYRB9t2NIkP/xqnvdqtIWX9vExOJFLyqBxJ/spHwqDl0OQRwIBVb8DnXSHlhNnJRIqljGwrI2dvw2bAvY3C6dggzOxIIiWSypFcmZcvdH0fun8CXv5w+Ff72Wyxy8xOJlLsvLNsP7EnUwn29+ble+ubHUekxFI5kmsT1QsGr4LQhpB+Gmb2sH8ukjXH7GQixcKWuHN8tNo+Tnv9vgaU0ThNxDQqR3LtgmvaP1X75kfty2vehhmdITne3FwiRVxGtpVn/hqndW9Skfb1NU4TMZPKkRSMpw90edv+/WxepeHo7/Yx259LzE4mUmS9+fM+Dp5Ko3xpb8beo3GaiNlUjuT6NOgOQ1dDhcZw4Rx8dT/8/AJYs81OJlKkbD5ylk/WHAJgfPeGBPp6mpxIRFSO5PqVrQ4Df4Zbh9iX174Hn3aEc0fMzSVSRFzIsvLM7O0YBvS4qRJt64aaHUlEUDmSG+XhDXdPhAdmgk8gHNsEU1vAnoVmJxNxeZOW7OPQ6TTCAnwYc089s+OIyF9UjqRw1L0HhvwKFZtCRjJ82wd+Gg05mWYnE3FJ6w+eYfrav8ZpPRoSWErjNBFXoXIkhadMFRiwGJoNty+v/xCmtYezh8zNJeJi0rNyGDXHPk574OYI2tQpb3YkEbmIypEULg8v6PAa9P4GSpWBE1thakvYNd/sZCIuY+LifcSdTSc80If/dKlrdhwR+QeVI3GMOp3sY7aIaMhMgdn94MeRkJ1hdjIRU607cIYZaw8D8EbPKAJ8NE4TcTUqR+I4QRHQ/0e442n78sZPYFo7OHPA3FwiJknLzGHUnG0APBRdmRa1QkxOJCJ5UTkSx3L3hHYvQZ/vwLccJOywj9l2zDE7mYjTjf9pD/HnLlAxqBTP361xmoirUjkS56jVDoaugSq3Q1YqfDcQvn8Csi+YnUzEKX6LPc3M3+MAmNgzCn9vD5MTiUh+VI7EeQLCoe/30HIUYIEtn8PHd8KpfWYnE3Go8xnZPDtnOwCP3FaF22sGm5xIRK5E5Uicy90D7nwBHpkHfuXh5G74qDVs/drsZCIO8/qivRxLukBE2VKM7hRpdhwRuQqVIzFHjTb2MVu1lpCdDvOHwvx/QVaa2clECtXqP0/x9Qb7OG1Sz0b4aZwm4vJUjsQ8pUPhkfnQ5j9gcYOtX8JHbSBxt9nJRApFSkY2z31nH6f1b16V26qXMzmRiFwLlSMxl5s7tHrWfiySfxic3mc/DmnL52AYZqcTuSGvLtzNieQMqpTz5dmOdcyOIyLXSOVIXEO1FvYxW407IeeC/Uy2uYMh87zZyUSuy4p9J5m1KR6LxT5O8/XSOE2kqFA5EtfhH2L/PKS2Y8HiDjtm2Q/WTthhdjKRAklOz2b0X+O0R2+vxq3VypqcSEQKQuVIXIubG7QYYf9k7YCKcCYWPm4LG6dpzCZFxisLd5OYkkm1YD+eaa9xmkhRY3o5Gj9+PLfccgulS5emfPnydOvWjX37rvy5NzNmzMBisVxy8fHxcVJicYoqzezfzVarA1gz4ccRMGcAZKSYnUzkipbtTuS7LfZx2uReUZTycjc7kogUkOnlaNWqVQwbNozff/+dpUuXkp2dTfv27UlLu/Ip3QEBAZw4cSL3cuTIESclFqfxKwe9v4H2r4KbB+yaZ//qkeN/mJ1MJE9J6VnEzLOPgQe1qE7TKhqniRRFph8huHjx4kuWZ8yYQfny5dm8eTMtW7bMdzuLxUJYWNg1PUZmZiaZmZm5yykpevehyHBzg+ZPQMRtMOdROHcIprW3F6ZbB4PFYnZCkVwv/7CbU+czqR7ix4i7apsdR0Suk+nvHP1TcnIyAGXLXvn/uFJTU6lSpQoRERF07dqVXbt25bvu+PHjCQwMzL1EREQUamZxgohbYOhqiOwC1iz46VmY9QhcSDI7mQgAS3YlMO+PY7hZ4M1ejfDx1DhNpKiyGIbrHOVqs9m49957SUpKYs2aNfmut27dOvbv309UVBTJyclMnjyZ1atXs2vXLipVqnTZ+nm9cxQREUFycjIBAQEO2RdxEMOA9VPh5xfAlg1BlaHnDKjU1Oxk4gLS0sDf3/7n1FTw83PO455Ny6L926s4nZrF0FY19BUhIg6SkpJCYGCgw39/u1Q5evzxx/npp59Ys2ZNniUnP9nZ2dStW5fevXszbty4q67vrL9ccaBjW+wHaJ87bD8eqd3L0GyYxmwlnFnl6Imv/+CHbcepVd6fH564Q+8aiTiIs35/u8xYbfjw4SxcuJAVK1YUqBgBeHp60qRJE2JjYx2UTlxOxZtgyGqo1w1sOfDzf+Dr3pB+1uxkUsL8tOMEP2w7jrubhckap4kUC6aXI8MwGD58OPPmzWP58uVUq1atwPdhtVrZsWMHFSpUcEBCcVk+gdBrBnR+E9y94c+fYEoLiFtvdjIpIc6kZvLC/J0APN6qBo0igswNJCKFwvRyNGzYMGbOnMlXX31F6dKlSUhIICEhgQsXLuSu07dvX2JiYnKXX3nlFX7++WcOHjzIli1bePjhhzly5AiPPfaYGbsgZrJY4JbH4LFlULYGpMTD9E6w5m2w2cxOJ8XcmAW7OJOWRZ3Q0jzRtqbZcUSkkJhejj788EOSk5Np3bo1FSpUyL18++23uevExcVx4sSJ3OVz584xaNAg6taty913301KSgpr166lXr16ZuyCuIIKUTBkFTToCYYVlr0EX90PaafNTibF1MLtx/lxxwnc3Sy8eX8jvD00ThMpLlzqgGxn0QHZxZhhwJbP7af652RA6QrQYxpUvd3sZOIEzjog+9T5TNq/vYpz6dn8u20tfaaRiJOUuAOyRQqFxQJN+8Gg5RBcG86fgM+6wKpJYLOanU6KAcMweGH+Ds6lZ1O3QgDD22icJlLcqBxJ8RRaHwatgEa9wbDBildhZndIPWl2Minivt92nCW7EvFwszC5VxReHnoZFSlu9FMtxZe3P9w3Bbp9CJ6+cHAlTLkDDq4yO5kUUSdTMhizwP5p/E/cWYv64YEmJxIRR1A5kuKv8UP2d5FC6kJqInzeFVa8rjGbFIhhGDw/bwfJF7KpHx7Av9rUMDuSiDiIypGUDOUj7cchNXkEMGDVG/aSlHLiqpuKAMz74xjL9pzE091+dpqnu14+RYor/XRLyeHlC13fh+6fgJc/HP7VPmaL/cXsZOLiElMyeOl7+zjtyba1iAzTWa4ixZnKkZQ8Ub1g8CoIbQjpp+0Hai97Gaw5ZicTF2QYBjFzd5CSkUPDioEMbaVxmkhxp3IkJVNwTfunat/8qH15zVv2U/6Tj5mbS1zOnM3xLN97Ei93N968vxEeGqeJFHv6KZeSy9MHurwNPaeDV2mIW2cfs/25xOxk4iJOJF/glR92A/D0XbWpHVra5EQi4gwqRyINusPQ1VChEVw4a//akZ9fAGu22cnERIZhMPq7HZzPzKFRRBCDWhT8S7FFpGhSORIBKFsdBi6FW4fYl9e+Z/8C26Q4c3OJaWZtOsqqP0/h5eHGm72iNE4TKUH00y7yNw9vuHsi3P8FeAdC/Eb7mG3vj2YnEyc7lnSBcQv3APBM+9rULK9xmkhJonIk8k/17rWP2So2hYxk+OYh+Gk05GSZnUycwDAMnpuzndTMHG6qHMTAO6qbHUlEnEzlSCQvZarCgMXQbLh9ef2H8Gl7OHvI1FjieF9tiGNN7Gm8PdyY3KsR7m4WsyOJiJOpHInkx8MLOrwGvb8BnyA4/gdMbQm75pudTBzk6Nl0Xv/RPk4b1aEO1UP8TU4kImZQORK5mjqdYOgaiIiGzBSY3Q9+HAnZGWYnk0Jksxk899120rKs3FK1DANu19lpIiWVypHItQiKgP4/wu1P2Zc3fgLT2sGZA6bGksLz5fojrD1wBh9PNyb11DhNpCRTORK5Vu6ecNfL0GcO+JaDhB32MduOOWYnkxsUdyad1xftBWB0x0iqBvuZnEhEzKRyJFJQte6yj9kqN4esVPhuIHz/b8i+YHYyuQ42m8GoOdu4kG0lulpZ+jaranYkETGZypHI9QgIh34/QMtRgAW2fAYft4VTf5qdTAro83WHWX/oLL5e7kzq2Qg3jdNESjyVI5Hr5e4Bd74Aj8wDvxA4uQs+agVbvzY7mVyjw6fTmLDYPk6L6RRJ5XK+JicSEVegciRyo2q0sY/ZqrWE7HSYPxTm/wuy0sxOJlfw9zgtI9tG8xrl6BNdxexIIuIiVI5ECkPpMHhkPrR+HixusPVL+KgNJO42O5nkY/raw2w8fA4/L3fe6BGlcZqI5FI5Eiksbu7Q+jno+z34h8HpffDxnbDlczAMs9PJRQ6eSmXiX+O0/3SuR0RZjdNE5H9UjkQKW7UW9jFbjTsh5wJ8/wTMHQyZqWYnE8BqM3hm9jYyc2y0qBVM71sjzI4kIi5G5UjEEfxDoM930HYMWNxhxyz7wdoJO8xOVuJNW3OQLXFJ+Ht7MKFHFBaLxmkicimVIxFHcXODFiPtn6xdOhzOxNpP99/0qcZsJok9eZ7JP9s/buHFLnWpGFTK5EQi4opUjkQcrUoz+5itVgewZsLCp2HOo5CRYnayEiXHamPk7O1k5dhoVTuE+2/WOE1E8qZyJOIMfuWg9zdw1zhw84Bdc+1fPXJ8q9nJSoyPfz3EtqNJlPbxYEKPhhqniUi+VI5EnMXNDW7/NwxYDIERcO4QTLsL1n+kMZuD/Zl4nreX2sdpY7rUo0Kgxmkikj+VIxFni7gFhqyGOp3BmgU/jYJZj8CFJLOTFUs5VhvPzN5GltXGnZHl6dm0ktmRRMTFqRyJmMG3LDz4JXScAG6esOcHmNoC4jebnazYmbr6INvjkwnw8WB8d43TROTqVI5EzGKxwG2Pw8AlEFQFkuLg0w6w7gON2QrJ3oQU3llmH6e93LU+oQE+JicSkaJA5UjEbBWbwtBfoV5XsGXDkufhm4cg/azZyYq0bKuNkbO2kW01aFc3lG6NK5odSUSKCJUjEVfgEwi9PoO7J4O7F+xbBFNawNENZicrsj757QC7jqcQ5OvJ690baJwmItfMJcrRBx98QNWqVfHx8SE6OpoNG678C2H27NlERkbi4+NDw4YNWbRokZOSijiQxQK3DoLHlkHZ6pASD592hDXvgM1mdroixbN8MlN+3Q/Ay/fWp3xpjdNE5Np5mB3g22+/ZcSIEUyZMoXo6GjeeecdOnTowL59+yhfvvxl669du5bevXszfvx4unTpwldffUW3bt3YsmULDRo0KNBjp6WBu3th7YlIIQloBI+sxvvnp/DYMweWjSXnwBoy754KvuXMTufS0tIANxvBd28nx2bQLjKMtjXD7deLSJHnrJ9li2GYe+RndHQ0t9xyC++//z4ANpuNiIgInnjiCUaPHn3Z+g888ABpaWksXLgw97rbbruNxo0bM2XKlDwfIzMzk8zMzNzllJQUIiIigGQgoFD3R6TwGDx202e82/E5SnlmEJ8STu/vprEmrrnZwVxa4B1/EnT7fqzpXhyf1hJburfZkUSk0KQAgSQnJxMQ4Ljf36aO1bKysti8eTPt2rXLvc7NzY127dqxbt26PLdZt27dJesDdOjQId/1AcaPH09gYGDuxV6MRFydhU+29OfWT5az51RtKgUcZ0W/LsTcMRkLGrPlxSs0mcDbYgE4u7S+ipGIXBdTx2qnT5/GarUSGhp6yfWhoaHs3bs3z20SEhLyXD8hISHfx4mJiWHEiBG5y3+/c3T8ODiweIoUkvqQtYLsZc/guetrXm87jnGPriGj88fgF2J2OJeRlWOl18fbiD1tkLa3AodWhePnZ3YqESlMKSkQHu74xzH9mCNn8Pb2xtv78v+D9PNDL55SNPj5Q68pULMFLHoG9yMr8Pv8dujxCVRraXY6l/DhklhiT5/HmubF2Z/r6+dbpBiyWp3zOKaO1YKDg3F3dycxMfGS6xMTEwkLC8tzm7CwsAKtL1KsNOkDg1ZASF1ITYTPu8LKCWBz0iuGi9oen8SHqw4AcPbnBtguaJwmItfP1HLk5eVF06ZN+eWXX3Kvs9ls/PLLLzRr1izPbZo1a3bJ+gBLly7Nd32RYqd8JAxaDk0eAcMGK8fbS9L5/EfLxVlmjpWRs7ZhtRncXT+c9D8rmB1JRIo40z/naMSIEXz88cd89tln7Nmzh8cff5y0tDQGDBgAQN++fYmJicld/8knn2Tx4sW8+eab7N27l5deeolNmzYxfPhws3ZBxPm8fKHr+9D9Y/D0g8O/wpQ74MBys5M53TvL9rP/ZCrB/t78p2N9s+OISDFg+jFHDzzwAKdOnWLMmDEkJCTQuHFjFi9enHvQdVxcHG5u/+twzZs356uvvuKFF17g+eefp1atWsyfP7/An3EkUixE3Q/hTWB2f0jcCV90hxYjoXUMuJv+4+1wf8SdY+pf47TX72tAkK+XyYlEpDgw/XOOzJCSkkJgoOM/J0HEabIv2L+TbdOn9uXKze0HawcW3+8Ty8i20vndXzlwKo37mlTk7Qcak5YG/v7221NTdUC2SHHjrN/fpo/VRKQQeJaCLm9Dz0/BqzTErbWP2fYvNTuZw7y99E8OnEqjfGlvxt5Tz+w4IlKMqByJFCcNesCQVVChEVw4C1/2hKVjwJptdrJCtfnIOT7+9SAA47s31DhNRAqVypFIcVOuBgxcCrcOsS//9l+YfjckHTU3VyG5kGXlmdnbsBnQ46ZKtK0bevWNREQKQOVIpDjy8Ia7J8L9X4B3IMRvsI/Z9i4yO9kNm/zzPg6dTiM0wJsxGqeJiAOoHIkUZ/XuhaGrIfwmyEiCb3rD4uchJ8vsZNdl4+GzfPrbIQAm9IgisJSnyYlEpDhSORIp7spUhUeXwG3D7Mu/fwCfdoBzh81MVWDpWTmMmr0Nw4AHbo6gTZ3yZkcSkWJK5UikJPDwgo6vQ+9vwCcIjm+BKS1h9/dmJ7tmExfv4/CZdCoE+vCfLnXNjiMixZjKkUhJUqcTDF0DlW6FzGSY9QgsGgXZGWYnu6LfD55hxtrDALzRI4oAH43TRMRxVI5ESpqgCBiwCG5/0r684SOYdhecOWBurnykZeYwas42AHrfWpmWtUNMTiQixZ3KkUhJ5O4Jd70CfeaAbzlI2A5TW8HO78xOdpk3Fu/l6NkLVAwqxX86a5wmIo6nciRSktW6yz5mq9wcss7DnEfhh6fsX0fiAtbGnubzdUcAmNgzCn/v4v99cSJiPpUjkZIuIBz6/QAtRwEW2DwdPmkHp/ebGis1M4dRc7YD8PBtlbm9ZrCpeUSk5FA5EhFw94A7X4BH5oJfCCTutI/Ztn1rWqTXF+3hWNIFKpUpRUwnjdNExHlUjkTkf2rcaR+zVW0B2WkwbzAsGAZZ6U6N8ev+U3y1Pg6AST0b4adxmog4kcqRiFyqdBj0XQCtnweLG/wxEz5uAyf3OOXhz2dk89xf47R+zarQrEY5pzyuiMjfVI5E5HJu7tD6OXtJ8g+FU3vhozb2omQYDn3o137cw/HkDCqX9eW5TpEOfSwRkbyoHIlI/qq1hKG/QfU2kHPBPmKbNxQyUx3ycCv3neSbjUexWGByr0b4emmcJiLOp3IkIlfmHwIPz4U7X7SP2bZ/Ax+1hoSdhfowyReyGf3dDgD6N6/KrdXKFur9i4hcK5UjEbk6Nzdo+Qz0/xFKh8OZ/fBJW9g0vdDGbOMW7iYhJYOq5Xx5toPGaSJiHpUjEbl2VZrbz2areRfkZMDCp+C7gZCRckN3u3xvInM2x+eO00p5uRdOXhGR66ByJCIF41cOHppl//oRi7v9K0c+agUntl3X3SWn/2+c9tgd1bi5qsZpImIulSMRKTg3N/sX1z66GAIj4OxB+6dqb/i4wGO2l3/YxcnzmVQP9mNk+zoOCiwicu1UjkTk+kXcCkNWQ527wZoFi56BWX3hQtI1bf7zrgTm/nEMNwtMvr8RPp4ap4mI+VSOROTG+JaFB7+CDuPBzRP2fA9TW8KxzVfc7FxaFs/Ps5/xNqhldW6qXMYZaUVErkrlSERunMUCzf4FA5dAUGVIOgLTOsC6/8t3zPbSD7s4nZpJzfL+PN2utpMDi4jkT+VIRApPxaYw5Feoew/YsmFJDHzzEKSfvWS1xTtPsGDrcdzdLLzZS+M0EXEtKkciUrhKBcH9X8Ddk8HdC/Ytso/Zjm4A4ExqJv/5a5w2pGV1GkUEmZdVRCQPKkciUvgsFrh1EAxcCmWqQfJRmN4JfvsvYxfs4ExaFrVD/XmyXS2zk4qIXEblSEQcJ7yx/Wy2+t3BlgNLx9B970iC3c7zZq/GeHtonCYirkflSEQcyycAen7K+bsmk4knd7pvZYX/izS07jI7mYhInlSORMThDODZQzfRNXMcR90qUjrrJMzoAqsng81mdjwRkUuoHImIw/2w/QQ/7Uwg1lKF1H7LIOoBMKywfBzM7A6pJ82OKCKSS+VIRBzq5PkMxiywn502/M6a1K0SDvdNha4fgEcpOLgCptwBh1abnFRExE7lSEQcxjAM/jNvJ0np2dSrEMCwNjXtN1gs0ORhGLwCQiIhNRE+7worJ4DNam5oESnxVI5ExGEWbD3O0t2JeLpbePP+Rni6/+Mlp3xdGLQcGj8Mhg1WjreXpPMJ5gQWEcHEcnT48GEGDhxItWrVKFWqFDVq1GDs2LFkZWVdcbvWrVtjsVguuQwdOtRJqUXkWiWmZDD2e/sZaU+2rUXdCgF5r+jlB90+sI/aPP3g8K/2MduB5U5MKyLyPx5mPfDevXux2WxMnTqVmjVrsnPnTgYNGkRaWhqTJ0++4raDBg3ilVdeyV329fV1dFwRKQDDMHh+7g6SL2TTsGIgQ1vVuPpGjR6E8Jtgdn84uQu+6A4tRkLrGHA37aVKREog015xOnbsSMeOHXOXq1evzr59+/jwww+vWo58fX0JCwtzdEQRuU7fbTnGL3tP4uXuxuRejfD45zgtPyG1YdAvsDgGNk+HXyfDkbXQ4xMIrOjY0CIif3GpY46Sk5MpW7bsVdf78ssvCQ4OpkGDBsTExJCenn7F9TMzM0lJSbnkIiKOkZCcwcs/2MdpT91VizphpQt2B56l4J53oMc08CoNcWvtY7b9Sws/rIhIHlymHMXGxvLee+8xZMiQK6730EMPMXPmTFasWEFMTAxffPEFDz/88BW3GT9+PIGBgbmXiIiIwowuIn8xDIPRc7dzPiOHRhFBDG5R/frvrGFPGLIKwqLgwln4sicsHQPW7MILLCKSB4thGEZh3uHo0aN54403rrjOnj17iIyMzF0+duwYrVq1onXr1nzyyScFerzly5fTtm1bYmNjqVEj7+MaMjMzyczMzF1OSUkhIiKC5ORkAgLyOUhURAps1sajPPvddrw83Fj07zuoWb6A7xrlJTsDfn4BNn5sX46Itr+rFHT5/+SkpYG/v/3Pqang53fjDy8iriMlJYXAwECH//4u9HJ06tQpzpw5c8V1qlevjpeXFwDHjx+ndevW3HbbbcyYMQM3t4K9mZWWloa/vz+LFy+mQ4cO17SNs/5yRUqSY0kX6Pj2as5n5hDTKZIh13IQdkHsXgALnoDMZPAJgvumQJ1Ol6yiciRSvDnr93ehH5AdEhJCSEjINa177Ngx2rRpQ9OmTZk+fXqBixHA1q1bAahQoUKBtxWRwmEYBqO/2875zByaVA7isRsZp+WnXlf7iG3Oo3B8C3z9INw2DNq9BB5ehf94IlJimXbM0bFjx2jdujWVK1dm8uTJnDp1ioSEBBISEi5ZJzIykg0bNgBw4MABxo0bx+bNmzl8+DDff/89ffv2pWXLlkRFRZm1KyIl3jcbj/Lr/tN4e9jPTnN3szjmgcpWg0eXwG3/si///gFM7wjnDjvm8USkRDLtVP6lS5cSGxtLbGwslSpVuuS2vyd92dnZ7Nu3L/dsNC8vL5YtW8Y777xDWloaERER9OjRgxdeeMHp+UXELv5cOq8u3A3AqA51qBHi79gH9PCCjuOhaguY/zgc2wxTWkLX96HKvY59bBEpEQr9mKOiQMcciRQOm83g4WnrWXvgDDdXKcO3Q5o57l2jvCTF2cds8RsByG4yGP8er5Jl9dYxRyLFkLN+f7vMqfwiUvR8uSGOtQfO4OPpxiRHjtPyE1QZBvwEtz8JgOcfH7H20buoUeaAc3OISLGiciQi1+Xo2XTGL9oDwHMdI6kWbNLbNO6ecNcr8NBsjFJlaRq+jS1DWuG+d645eUSkyFM5EpECs9kMRs3ZRnqWlVurlaVfs6pmR4La7bnQbw2/HmlGgPd5fH4YAD88BdkXzE4mIkWMypGIFNgXvx/h94NnKeXpzqSeUbg5e5yWD6N0Rdp8tpDXfh2JgcX+/WyftIPT+82OJiJFiMqRiBTI4dNpTPhpLwAxd0dSpZxrHfVsNTx4YfkYMnt+B77BkLgTpraCbd+aHU1EigiVIxG5ZjabwbNztnMh20qz6uV4OLqK2ZHyZa3WFoausZ/yn50G8wbDgmGQdeUvqhYRUTkSkWs2Y+1hNhw+i5+XOxNdaJyWr4AK0HcBtBoNWOCPmfDxnXByr9nJRMSFqRyJyDU5eCqViUv+HqfVJaKsr8mJrpGbO7SJsZck/1A4tQc+ag1/fGl2MhFxUSpHInJVVpvBqDnbyci2cUfNYPpEVzY7UsFVb2Ufs1VvDTkXYMG/YN5QyEw1O5mIuBiVIxG5qk/XHGLzkXP4e3swoUdDLBYXH6flx788PDwP7nwBLG6w7Wv4uA0k7DQ7mYi4EJUjEbmi2JOpTPp5HwAvdK5LpTJFZJyWHzc3aDkK+i2E0hXg9J/wSVvYNB1K3rcpiUgeVI5EJF9Wm8Ezs7eRlWOjZe0QHrglwuxIhafq7fYxW812kJMBC5+C7wZCRorZyUTEZCpHIpKvj389yNajSZT29mBC9yI8TsuPXzA8NBvavQwWd9j5HXzUCk5sMzuZiJhI5UhE8rQ/8Txv/fwnAC92qUd4UCmTEzmImxvc8ZT9C2wDKsHZg/ZP1d7wscZsIiWUypGIXCbHamPk7G1kWW20qRNCr5srmR3J8SpHw9BfoXYnsGbBomdgdj/ISDY7mYg4mcqRiFxm6uqDbI9PprSPB+O7RxW/cVp+fMtC76+hw+vg5gm7F8CUFnBss9nJRMSJVI5E5BJ7E1J4Z5l9nPbSPfUJC/QxOZGTWSzQbBg8ugSCKkPSEZjWAdb9n8ZsIiWEypGI5Mq22nhm9jayrQbt6pan+00VzY5knkpNYcivUPcesGXDkhj4pg+knzU7mYg4mMqRiOT6cOUBdh5LIbCUJ6/fVwzPTiuoUkFw/xfQaRK4e8G+H2FqSzi60exkIuJAKkciAsDu4ym8+8t+AF7pWp/yASVsnJYfiwWiB8PAn6FMNUg+CtM7wm//BZvN7HQi4gAqRyJCVo59nJZjM2hfL5R7G4WbHcn1hDeBIauhfnew5cDSMfD1g5B2xuxkIlLIVI5EhA9WxLL7RAplfD15TeO0/PkEQM9Pocvb4O4N+5fAlDvgyFqzk4lIIVI5Einhdh5L5oMVsQC80rUBIaW9TU7k4iwWuPlRGPQLlKsJ54/DjC6werLGbCLFhMqRSAl28Tjt7oZhdImqYHakoiOsIQxeBVEPgGGF5ePgyx6QesrsZCJyg1SOREqw95bvZ2/Cecr5eTGuawON0wrK2x/umwr3vg8epeDAcphyOxxabXYyEbkBKkciJdT2+CT+b+UBAMZ1a0A5f43TrovFAjc9AoNXQHAdSE2Ez7vCyglgs5qdTkSug8qRSAmUmWNl5KxtWG0GXaIqcHdDjdNuWPm69oLU+GEwbLByPHzRDc4nmJ1MRApI5UikBHpn2X72n0wl2N+LV7o2MDtO8eHlB90+sI/aPP3s47Upd9jHbSJSZKgciZQwW48mMXWVfZz2areGlPXzMjlRMdToQRi8EsrXh7RT8EV3+GUcWHPMTiYi10DlSKQEyci2MnLWVmwGdGscTscGYWZHKr5CattP92/aHzDg18nw2T2QctzsZCJyFSpHIiXI20v/5MCpNEJKe/PSvfXNjlP8eZaCe/4LPaaBlz/ErbWP2fYvNTuZiFyBypFICbH5yDk+/vUgAK/f15AgX43TnKZhT/tXj4Q1hPQz8GVP+9ePWLPNTiYieVA5EikBMrKtjJq9DZsB3ZtU5K56oWZHKnnK1YCBy+CWQfbl3/4LMzpD0lFzc4nIZVSOREqAyUv2cfB0GqEB3oy9R+M003j6QOfJ0Osz8A6Ao+vtY7a9i8xOJiIXUTkSKeY2Hj7LtN8OATChexSBvp4mJxLqd7OP2cKbQEYSfNMbFj8POVlmJxMRTC5HVatWxWKxXHKZMGHCFbfJyMhg2LBhlCtXDn9/f3r06EFiYqKTEosULRey7OM0w4BeTSvRJrK82ZHkb2WrwaM/w23/si///gFM7wjnDpsaS0Rc4J2jV155hRMnTuRennjiiSuu//TTT/PDDz8we/ZsVq1axfHjx+nevbuT0ooULROX7OXwmXQqBPrwQpd6ZseRf/Lwgo7j4cGvwCcQjm2GKS1h9/dmJxMp0UwvR6VLlyYsLCz34ufnl++6ycnJTJs2jbfeeos777yTpk2bMn36dNauXcvvv//uxNQiru/3g2eY/tthACb0iCKwlMZpLiuyMwxdA5VugcxkmPUILBoFOZlmJxMpkUwvRxMmTKBcuXI0adKESZMmkZOT/yfIbt68mezsbNq1a5d7XWRkJJUrV2bdunX5bpeZmUlKSsolF5HiLC0zh2fnbAeg960RtKodYnIiuaqgyjDgJ2j+b/vyho9gWns4e9DcXCIlkKnl6N///jfffPMNK1asYMiQIbz++us8++yz+a6fkJCAl5cXQUFBl1wfGhpKQkL+X+44fvx4AgMDcy8RERGFtQsiLumNxXuJO5tOxaBSPH93XbPjyLVy94T24+ChWVCqLJzYah+z7ZxrdjKREqXQy9Ho0aMvO8j6n5e9e/cCMGLECFq3bk1UVBRDhw7lzTff5L333iMzs3DfSo6JiSE5OTn3cvSoPldEiq+1B07z+bojALzRI4rSPhqnFTm1O9jHbJWbQdZ5mDMAFj4N2RlmJxMpETwK+w5HjhxJ//79r7hO9erV87w+OjqanJwcDh8+TJ06dS67PSwsjKysLJKSki559ygxMZGwsPy/I8rb2xtvb+9ryi9SlKVeNE7rE12ZO2oFm5xIrltgRei3EFa+Dr++BZs+haMbodcMCK5pdjqRYq3Qy1FISAghIdd3fMPWrVtxc3OjfPm8Tzdu2rQpnp6e/PLLL/To0QOAffv2ERcXR7Nmza47s0hxMX7RHuLPXaBSmVLEaJxW9Ll7QNsxUOV2mDsYEnfAR62gyzsQ1cvsdCLFlmnHHK1bt4533nmHbdu2cfDgQb788kuefvppHn74YcqUKQPAsWPHiIyMZMOGDQAEBgYycOBARowYwYoVK9i8eTMDBgygWbNm3HbbbWbtiohLWLP/NF+ujwNgYs8o/L0L/f99xCw129rHbFVbQFYqzH0MFgyHrHSzk4kUS6a9enp7e/PNN9/w0ksvkZmZSbVq1Xj66acZMWJE7jrZ2dns27eP9PT/vQC8/fbbuLm50aNHDzIzM+nQoQP/93//Z8YuiLiM8xnZPPedfZzWt1kVmtfQOK3YCagAfRfAqomw6g344wv75yL1mgEhlx+GICLXz2IYhmF2CGdLSUkhMDCQ5ORkAgICzI4jcsNi5m7n6w1HqVzWl5+ebIFfCX3XKC0N/P3tf05NhSt8bFrRdnAVzB0EqYng6Qud34TGD5mdSsThnPX72/TPORKRG7Pqz1N8vcF+BuaknlElthiVKNVb2cds1VtDdjrMfxzmPQ5ZaWYnEykWVI5EirCUjGxG/zVOG3B7VaKrlzM5kTiNf3l4eB7c+QJY3GDbV/BRa0jcbXYykSJP5UikCHt14W5OJGdQtZwvz3aINDuOOJubG7QcZT/lv3QFOP0nfNwGNn8GJe+ICZFCo3IkUkSt2HuSWZvisVhgcq9GlPJyNzuSmKXq7fYxW812kJMBP/zbfkxS5nmzk4kUSSpHIkVQcno2o+fax2kDb6/GzVXLmpxITOcXDA/NhnYvg8UddsyGqa3gxHazk4kUOSpHIkXQKwt3k5iSSfVgP57poNO45S9ubnDHU/YvsA2oBGcPwCftYOMnGrOJFIDKkUgRs2x3It9ticfNApPvb4SPp8Zp8g+Vo2Hor1C7E1gz4ceRMLs/ZCSbnUykSFA5EilCktKziJm3A4BBLapzU+UyJicSl+VbFnp/De1fAzcP2D0fpraEY1vMTibi8lSORIqQl77fxanzmdQI8ePpu2qbHUdcncUCzYfDoz9DUGU4dximtYffp2jMJnIFKkciRcSSXQnM33ocNwu8eX9jjdPk2lVqCkNWQ2QXsGXD4ufg24fhwjmzk4m4JJUjkSLgbFoW//lrnDa0VQ0aRwSZG0iKnlJl4IGZ0GkSuHvB3oUwpSXEbzI7mYjLUTkSKQLGfr+L06lZ1A7158l2tcyOI0WVxQLRg2Hgz1CmGiTHwacdYO17GrOJXETlSMTFLdpxgh+2HcfdzcLkXo3w9tA4TW5QeBMYsgrq3we2HPj5Bfj6QUg/a3YyEZegciTiwk6nZvLC/J0A/Kt1DaIqBZkbSIoPn0DoOR06vwXu3vDnYphyB8T9bnYyEdOpHIm4sDELdnI2LYvIsNI8cafGaVLILBa4ZSAM+gXK1YSUYzD9bvj1LbDZzE4nYhqVIxEXtXD7cRbtSMDjr3Gal4d+XMVBwhrC4JXQ8H4wrPDLy/BlT0g9ZXYyEVPo1VbEBZ06n8mLf43ThrWpSYOKgSYnkmLPuzR0/wjufR88SsGBX+xjtsNrzE4m4nQqRyIuxjAMXpi/g3Pp2dSrEMCwNjXNjiQlhcUCNz0Cg5ZDcB1ITYDP7oFVE8FmNTudiNOoHIm4mO+3HWfJrkQ83TVOE5OE1oPBK6BxHzBssOI1+OI+OJ9odjIRp9CrrogLOZmSwZgFuwB44s5a1AsPMDmRlFheftDt/6DbFPD0hUOr7GO2gyvNTibicCpHIi7CMAyen7eD5AvZNKgYwOOta5gdSQQa94bBq6B8PUg7CZ93g+WvgTXH7GQiDqNyJOIi5v1xjGV7TuLpbuHNXo3xdNePp7iIkNr245Bu6gcYsHoifH4vpJwwO5mIQ+jVV8QFJCRn8NL39nHaU+1qUyestMmJRP7BsxTc+y70mAZe/nDkN5hyO+xfZnYykUKnciRiMsMwiJm7nZSMHKIqBTKkZXWzI4nkr2FPGLLa/tlI6Wfgyx6w7CWN2aRYUTkSMdnszfGs2HcKL3c33uzVCA+N08TVlasBA5fBLY/Zl9e8DTM6Q3K8ublEColehUVMdCL5AuN+2A3AiPa1qRWqcZoUEZ4+0PlN6PUZeAfA0d/tZ7PtW2x2MpEbpnIkYhLDMHjuux2cz8yhSeUgBrXQOE2KoPrd7GO28CZw4Rx8/QAs+Q/kZJmdTOS6qRyJmOTbjUdZ/ecpvDzcmNSzEe5uFrMjiVyfstXg0SUQ/bh9ed37ML0TnDtibi6R66RyJGKCY0kXePXHPQCMal+HmuX9TU4kcoM8vKHTBHjwK/AJhGObYGoL2LPQ7GQiBaZyJOJkhmHw3JztpGbm0LRKGR69o5rZkUQKT2RnGLoGKt4MGcnwbR/46TnIyTQ7mcg1UzkScbKvNsSxJvY0Pp5uTOoZpXGaFD9BleHRxdD8Cfvy+ikwrT2cPWhuLpFrpHIk4kRHz6bz2l/jtGc7RFI9ROM0KabcPaH9q/DQLChVBk5shamtYNc8s5OJXJXKkYiT2GwGz87ZTnqWlVurlqV/86pmRxJxvNod7GO2iNsgMwVm94eFIyA7w+xkIvlSORJxkpnrj7Du4BlKebozsWcUbhqnSUkRWAn6/wh3jLAvb5oG09rBmQPm5hLJh8qRiBPEnUln/KK9AIzuFEnVYD+TE4k4mbsHtBsLD38HvsGQsAOmtoQdc8xOJnIZ08rRypUrsVgseV42btyY73atW7e+bP2hQ4c6MblIwdhsBs/M2caFbCu3VS/LI7dVMTuSiHlqtrOP2arcAVmp8N1A+P4JyL5gdjKRXKaVo+bNm3PixIlLLo899hjVqlXj5ptvvuK2gwYNumS7iRMnOim1SMF9tu4wGw6dxdfLnUk9G2mcJhJQAfougFbPARbY8jl8fCec2md2MhEAPMx6YC8vL8LCwnKXs7OzWbBgAU888QQWy5V/efj6+l6yrYirOnQ6jTcW28dpMXfXJaKsr8mJRFyEuwe0eR6qNIfvBsHJ3fBRa+j8FjTubXY6KeFc5pij77//njNnzjBgwICrrvvll18SHBxMgwYNiImJIT09/YrrZ2ZmkpKScslFxNGsNoNRs7eRkW3j9prl6HNrZbMjibie6q3tY7ZqrSA7HeYPhfn/gqw0s5NJCeYy5WjatGl06NCBSpUqXXG9hx56iJkzZ7JixQpiYmL44osvePjhh6+4zfjx4wkMDMy9REREFGZ0kTxN/+0Qm46cw8/LnTd66Ow0kXyVDoVH5kGb/4DFDbZ+CR+1gcTdZieTEspiGIZRmHc4evRo3njjjSuus2fPHiIjI3OX4+PjqVKlCrNmzaJHjx4Ferzly5fTtm1bYmNjqVGjRp7rZGZmkpn5v4+uT0lJISIiguTkZAICAgr0eCLX4sCpVO7+769k5tgY370hvfWukVOkpYH/X5+rmZoKfjopsOg5vAa+ewzOnwAPH7h7EjR5BK5yuIWUDCkpKQQGBjr893ehH3M0cuRI+vfvf8V1qlevfsny9OnTKVeuHPfee2+BHy86OhrgiuXI29sbb2/vAt+3yPWw2gyemb2NzBwbLWoF8+AteqdS5JpVvcM+Zps7GA78Yj+T7dCv0OUt8C5tdjopIQq9HIWEhBASEnLN6xuGwfTp0+nbty+enp4FfrytW7cCUKFChQJvK+IIn/x6kD/ikijt7cEbPaKueoKBiPyDXzD0mQO/vQPLX4Uds+D4Fug1A8Iamp1OSgDTjzlavnw5hw4d4rHHHrvstmPHjhEZGcmGDRsAOHDgAOPGjWPz5s0cPnyY77//nr59+9KyZUuioqKcHV3kMrEnz/Pm0j8BeKFLXcKDSpmcSKSIcnODFiNgwCIIqAhnYuHjtrBxGhTu0SAilzG9HE2bNo3mzZtfcgzS37Kzs9m3b1/u2WheXl4sW7aM9u3bExkZyciRI+nRowc//PCDs2OLXCbHamPk7O1k5dhoXSeE+2/WOE3khlW+zT5mq90RrJnw4wiYMwAyks1OJsVYoR+QXRQ464AuKVn+b2UsExfvo7SPB0ufbkVYoI/ZkUocHZBdjBkGrPsAlo0FWw6UqWofs4U3MTuZOJGzfn+b/s6RSHGwL+E87yzdD8DYe+qrGIkUNosFmg+HR5dAYGU4dximtYf1UzVmk0KnciRyg7KtNp6ZvY0sq422keXpcVNFsyOJFF+VboahqyGyC1iz4Kdn4duH4cI5s5NJMaJyJHKDpqw8wI5jyQSW8uT17g11dpqIo5UqAw/MhI5vgJsn7F0IU1tC/Cazk0kxoXIkcgP2nEjh3eX2cdrL99YnNEDjNBGnsFjgtqEw8Gf78UdJcfBpB1j7nsZscsNUjkSuU7bVxshZ28i2GrSvF0rXxuFmRxIpeSreBENWQ71u9gO1f34Bvn4Q0s+anUyKMJUjkev0wYpYdp9IIcjXk1fva6BxmohZfALtZ651fhPcveHPxTClBcT9bnYyKaJUjkSuw67jyby/PBaAV7o2oHxpjdNETGWxwC2PwWPLoGwNSImH6XfDr2+BzWZ2OiliVI5ECigrxz5Oy7EZdGoQxj1R+uoaEZdRIQqGrIKGvcCwwi8vw1e9IO202cmkCFE5Eimg95fvZ2/Cecr6eTGum8ZpIi7HuzR0/xjueRc8fCB2GUy5Aw6vMTuZFBEqRyIFsCM+mQ9WHgBgXNcGBPt7m5xIRPJksUDTfjBoOQTXhvMn4LN7YNUksFnNTicuTuVI5Bpl5lgZOXsrVptB56gKdNY4TcT1hdaHwSuhUW8wbLDiVfjiPjifaHYycWEqRyLX6L/L9vNnYirB/l6M69rA7Dgicq28/OC+KdDtQ/D0hUOr7GO2gyvNTiYuSuVI5BpsO5rElFX2cdqr3RpS1s/L5EQiUmCNH4JBKyCkLqSdhM+7wYrXNWaTy6gciVxFRraVkbO3YTOga+NwOjYIMzuSiFyv8pH245Bu6gsYsOoN+OxeSDlhdjJxISpHIlfx9rI/iT2ZSkhpb166p77ZcUTkRnn5wr3vQfdPwMsfjqyxj9lil5mdTFyEypHIFWw+co6PVx8E4PX7GlJG4zSR4iOqFwxeBaENIf00zOwBy14Ca47ZycRkKkci+cjItjLqr3HafU0qcle9ULMjiUhhC65p/1Ttmwfal9e8DTM6Q3K8ubnEVCpHIvl48+d9HDydRnmN00SKN08f6PIW9JwOXqXh6O/2MdufS8xOJiZRORLJw6bDZ/lkzSEAJvRoSKCvp8mJRMThGnSHoauhQmO4cA6+uh+W/Aes2WYnEydTORL5hwtZVp6ZvQ3DgJ5NK3FnpMZpIiVG2eow8GeIHmpfXvc+fNoRzh0xN5c4lcqRyD9MXLKXw2fSCQvw4cUu9cyOIyLO5uENnd6AB2aCTyAc2wRTW8CehWYnEydRORK5yPqDZ5j+22Hgr3FaKY3TREqsuvfAkF+hYlPISIZv+8BPoyEn0+xk4mAqRyJ/Sc/KYdSc7QA8eEsEreuUNzmRiJiuTBUYsBiaDbcvr/8QprWHswfNzSUOpXIk8pc3ftpL3Nl0wgN9+E/numbHERFX4eEFHV6D3t9AqTJwYitMbQW75pmdTBxE5UgEWHvgNJ+tsx9w+UbPKEr7aJwmIv9QpxMMXQMR0ZCZArP7w8IRkJ1hdjIpZCpHUuKlZubw7F/jtIeiK9OiVojJiUTEZQVWgv4/wh1P25c3TYNp7eDMAXNzSaFSOZISb/yiPcSfu0DFoFI8f7fGaSJyFe6e0O4l6PMd+JaDhB0wtSXsmGN2MikkKkdSoq3Zf5ov18cBMKlnFP7eHiYnEpEio1Y7+5ityu2QlQrfDYTvn4DsC2YnkxukciQl1vmMbJ77zj5Oe+S2KjSvGWxyIhEpcgLCoe/30PJZwAJbPoeP74RT+8xOJjdA5UhKrNcX7eFY0gUiypZidKdIs+OISFHl7gF3/gcemQd+5eHkbvioNWz92uxkcp1UjqREWvXnKb7ecBSAST0b4adxmojcqBpt7GO2ai0hOx3mD4X5/4KsNLOTSQGpHEmJk5KRzei/xmn9m1flturlTE4kIsVG6VB4ZD60+Q9Y3GDrl/BRG0jcbXYyKQCVIylxXl24mxPJGVQp58uzHeuYHUdEihs3d2j1rP1YJP8wOL3PfhzSls/BMMxOJ9dA5UhKlBV7TzJrUzwWi32c5uulcZqIOEi1FvYxW422kHPBfibb3MGQed7sZHIVKkdSYiSnZzN6rn2c9ujt1bi1WlmTE4lIsecfAn3mQNuxYHGHHbPsB2sn7DA7mVyBypGUGC8v3EViSibVgv14pr3GaSLiJG5u0GKE/ZO1AyrCmVj4uC1snKYxm4tyWDl67bXXaN68Ob6+vgQFBeW5TlxcHJ07d8bX15fy5cszatQocnJyrni/Z8+epU+fPgQEBBAUFMTAgQNJTU11wB5IcbJsdyJztxzDYoHJvaIo5eVudiQRKWmqNLOP2Wp1AGsm/DgC5gyAjBSzk8k/OKwcZWVl0atXLx5//PE8b7darXTu3JmsrCzWrl3LZ599xowZMxgzZswV77dPnz7s2rWLpUuXsnDhQlavXs3gwYMdsQtSTCSlZxEzz/4W9qAW1WlaReM0ETGJb1no/Q20fxXcPGDXPPtXjxz/w+xkchGLYTj2Pb0ZM2bw1FNPkZSUdMn1P/30E126dOH48eOEhoYCMGXKFJ577jlOnTqFl5fXZfe1Z88e6tWrx8aNG7n55psBWLx4MXfffTfx8fGEh4fnmSEzM5PMzMzc5eTkZCpXrszRo0cJCAgopD0VV/XcnG38uCOBqsG+zBnaHB9PvWtUXKWlwd8vA8ePg5+fuXlErih+MywYBinx4OYJbV+EpgPAYjE7mctKSUkhIiKCpKQkAgMDHfdAhoNNnz7dCAwMvOz6F1980WjUqNEl1x08eNAAjC1btuR5X9OmTTOCgoIuuS47O9twd3c35s6dm2+GsWPHGoAuuuiiiy666FIMLgcOHChwHykI085jTkhIyH3H6G9/LyckJOS7Tfny5S+5zsPDg7Jly+a7DUBMTAwjRozIXU5KSqJKlSrExcU5tnm6mL8bd0l7x0z7rf0uCbTf2u+S4O/JT9myjj08okDlaPTo0bzxxhtXXGfPnj1ERrrW91R5e3vj7e192fWBgYEl6h/V3wICArTfJYj2u2TRfpcsJXW/3dwce7J9gcrRyJEj6d+//xXXqV69+jXdV1hYGBs2bLjkusTExNzb8tvm5MmTl1yXk5PD2bNn891GREREpCAKVI5CQkIICQkplAdu1qwZr732GidPnswdlS1dupSAgADq1auX7zZJSUls3ryZpk2bArB8+XJsNhvR0dGFkktERERKNoe9LxUXF8fWrVuJi4vDarWydetWtm7dmvuZRO3bt6devXo88sgjbNu2jSVLlvDCCy8wbNiw3BHYhg0biIyM5NixYwDUrVuXjh07MmjQIDZs2MBvv/3G8OHDefDBB/M9Uy0v3t7ejB07Ns9RW3Gm/dZ+lwTab+13SaD9dux+O+xU/v79+/PZZ59ddv2KFSto3bo1AEeOHOHxxx9n5cqV+Pn50a9fPyZMmICHh/0NrZUrV9KmTRsOHTpE1apVAfuHQA4fPpwffvgBNzc3evTowbvvvou/v78jdkNERERKGId/zpGIiIhIUaLvVhMRERG5iMqRiIiIyEVUjkREREQuonIkIiIicpFiWY5ee+01mjdvjq+vL0FBQXmuExcXR+fOnfH19aV8+fKMGjWKnJycK97v2bNn6dOnDwEBAQQFBTFw4MDcjyZwRStXrsRiseR52bhxY77btW7d+rL1hw4d6sTkN65q1aqX7cOECROuuE1GRgbDhg2jXLly+Pv706NHj9wPJi0KDh8+zMCBA6lWrRqlSpWiRo0ajB07lqysrCtuVxSf7w8++ICqVavi4+NDdHT0ZR8o+0+zZ88mMjISHx8fGjZsyKJFi5yUtHCMHz+eW265hdKlS1O+fHm6devGvn37rrjNjBkzLntefXx8nJS4cLz00kuX7cPVvoGhqD/XkPfrl8ViYdiwYXmuX1Sf69WrV3PPPfcQHh6OxWJh/vz5l9xuGAZjxoyhQoUKlCpVinbt2rF///6r3m9BXx/yUizLUVZWFr169eLxxx/P83ar1Urnzp3Jyspi7dq1fPbZZ8yYMYMxY8Zc8X779OnDrl27WLp0KQsXLmT16tUMHjzYEbtQKJo3b86JEycuuTz22GNUq1aNm2+++YrbDho06JLtJk6c6KTUheeVV165ZB+eeOKJK67/9NNP88MPPzB79mxWrVrF8ePH6d69u5PS3ri9e/dis9mYOnUqu3bt4u2332bKlCk8//zzV922KD3f3377LSNGjGDs2LFs2bKFRo0a0aFDh8s+Pf9va9eupXfv3gwcOJA//viDbt260a1bN3bu3Onk5Ndv1apVDBs2jN9//52lS5eSnZ1N+/btSUtLu+J2AQEBlzyvR44ccVLiwlO/fv1L9mHNmjX5rlscnmuAjRs3XrLPS5cuBaBXr175blMUn+u0tDQaNWrEBx98kOftEydO5N1332XKlCmsX78ePz8/OnToQEZGRr73WdDXh3w59GttTTZ9+nQjMDDwsusXLVpkuLm5GQkJCbnXffjhh0ZAQICRmZmZ533t3r3bAIyNGzfmXvfTTz8ZFovFOHbsWKFnd4SsrCwjJCTEeOWVV664XqtWrYwnn3zSOaEcpEqVKsbbb799zesnJSUZnp6exuzZs3Ov27NnjwEY69atc0BC55g4caJRrVq1K65T1J7vW2+91Rg2bFjustVqNcLDw43x48fnuf79999vdO7c+ZLroqOjjSFDhjg0pyOdPHnSAIxVq1blu05+r39FydixY41GjRpd8/rF8bk2DMN48sknjRo1ahg2my3P24vDcw0Y8+bNy1222WxGWFiYMWnSpNzrkpKSDG9vb+Prr7/O934K+vqQn2L5ztHVrFu3joYNGxIaGpp7XYcOHUhJSWHXrl35bhMUFHTJOy7t2rXDzc2N9evXOzxzYfj+++85c+YMAwYMuOq6X375JcHBwTRo0ICYmBjS09OdkLBwTZgwgXLlytGkSRMmTZp0xbHp5s2byc7Opl27drnXRUZGUrlyZdatW+eMuA6RnJx8Td9eXVSe76ysLDZv3nzJ8+Tm5ka7du3yfZ7WrVt3yfpg/3kv6s8rcNXnNjU1lSpVqhAREUHXrl3zfX1zZfv37yc8PJzq1avTp08f4uLi8l23OD7XWVlZzJw5k0cffRSLxZLvesXhub7YoUOHSEhIuOT5DAwMJDo6Ot/n83peH/JToO9WKy4SEhIuKUZA7nJCQkK+2/z9HXB/8/DwoGzZsvlu42qmTZtGhw4dqFSp0hXXe+ihh6hSpQrh4eFs376d5557jn379jF37lwnJb1x//73v7npppsoW7Ysa9euJSYmhhMnTvDWW2/luX5CQgJeXl6XHaMWGhpaZJ7ff4qNjeW9995j8uTJV1yvKD3fp0+fxmq15vnzu3fv3jy3ye/nvag+rzabjaeeeorbb7+dBg0a5LtenTp1+PTTT4mKiiI5OZnJkyfTvHlzdu3addXXAFcRHR3NjBkzqFOnDidOnODll1+mRYsW7Ny5k9KlS1+2fnF7rgHmz59PUlLSFb/0vTg81//093NWkOfzel4f8lNkytHo0aN54403rrjOnj17rnqwXnFwPX8X8fHxLFmyhFmzZl31/i8+jqphw4ZUqFCBtm3bcuDAAWrUqHH9wW9QQfZ7xIgRuddFRUXh5eXFkCFDGD9+fJH7LqLreb6PHTtGx44d6dWrF4MGDbritq76fEvehg0bxs6dO6947A3Yv6i7WbNmucvNmzenbt26TJ06lXHjxjk6ZqHo1KlT7p+joqKIjo6mSpUqzJo1i4EDB5qYzHmmTZtGp06drvj9ocXhuXY1RaYcjRw58orNGaB69erXdF9hYWGXHb3+91lJYWFh+W7zzwO6cnJyOHv2bL7bOMr1/F1Mnz6dcuXKce+99xb48aKjowH7OxFm/rK8kX8D0dHR5OTkcPjwYerUqXPZ7WFhYWRlZZGUlHTJu0eJiYlOf37/qaD7ffz4cdq0aUPz5s356KOPCvx4rvJ85yU4OBh3d/fLziK80vMUFhZWoPVd2fDhw3NPBinoOwKenp40adKE2NhYB6VzvKCgIGrXrp3vPhSn5xrs3z+6bNmyAr+LWxye67+fs8TERCpUqJB7fWJiIo0bN85zm+t5fchXgY5QKmKudkB2YmJi7nVTp041AgICjIyMjDzv6+8Dsjdt2pR73ZIlS4rEAdk2m82oVq2aMXLkyOvafs2aNQZgbNu2rZCTOc/MmTMNNzc34+zZs3ne/vcB2XPmzMm9bu/evUXugOz4+HijVq1axoMPPmjk5ORc1324+vN96623GsOHD89dtlqtRsWKFa94QHaXLl0uua5Zs2ZF6iBdm81mDBs2zAgPDzf+/PPP67qPnJwco06dOsbTTz9dyOmc5/z580aZMmWM//73v3neXhye64uNHTvWCAsLM7Kzswu0XVF8rsnngOzJkyfnXpecnHxNB2QX5PUh3zwFWruIOHLkiPHHH38YL7/8suHv72/88ccfxh9//GGcP3/eMAz7P5wGDRoY7du3N7Zu3WosXrzYCAkJMWJiYnLvY/369UadOnWM+Pj43Os6duxoNGnSxFi/fr2xZs0ao1atWkbv3r2dvn8FtWzZMgMw9uzZc9lt8fHxRp06dYz169cbhmEYsbGxxiuvvGJs2rTJOHTokLFgwQKjevXqRsuWLZ0d+7qtXbvWePvtt42tW7caBw4cMGbOnGmEhIQYffv2zV3nn/ttGIYxdOhQo3Llysby5cuNTZs2Gc2aNTOaNWtmxi5cl/j4eKNmzZpG27Ztjfj4eOPEiRO5l4vXKerP9zfffGN4e3sbM2bMMHbv3m0MHjzYCAoKyj379JFHHjFGjx6du/5vv/1meHh4GJMnTzb27NljjB071vD09DR27Nhh1i4U2OOPP24EBgYaK1euvOR5TU9Pz13nn/v98ssvG0uWLDEOHDhgbN682XjwwQcNHx8fY9euXWbswnUZOXKksXLlSuPQoUPGb7/9ZrRr184IDg42Tp48aRhG8Xyu/2a1Wo3KlSsbzz333GW3FZfn+vz587m/nwHjrbfeMv744w/jyJEjhmEYxoQJE4ygoCBjwYIFxvbt242uXbsa1apVMy5cuJB7H3feeafx3nvv5S5f7fXhWhXLctSvXz8DuOyyYsWK3HUOHz5sdOrUyShVqpQRHBxsjBw58pJ2vmLFCgMwDh06lHvdmTNnjN69exv+/v5GQECAMWDAgNzC5cp69+5tNG/ePM/bDh06dMnfTVxcnNGyZUujbNmyhre3t1GzZk1j1KhRRnJyshMT35jNmzcb0dHRRmBgoOHj42PUrVvXeP311y95V/Cf+20YhnHhwgXjX//6l1GmTBnD19fXuO+++y4pFq5u+vTpef67v/gN4uLyfL/33ntG5cqVDS8vL+PWW281fv/999zbWrVqZfTr1++S9WfNmmXUrl3b8PLyMurXr2/8+OOPTk58Y/J7XqdPn567zj/3+6mnnsr9OwoNDTXuvvtuY8uWLc4PfwMeeOABo0KFCoaXl5dRsWJF44EHHjBiY2Nzby+Oz/XflixZYgDGvn37LrutuDzXf/+e/efl732z2WzGiy++aISGhhre3t5G27ZtL/v7qFKlijF27NhLrrvS68O1shiGYRRsECciIiJSfJXIzzkSERERyY/KkYiIiMhFVI5ERERELqJyJCIiInIRlSMRERGRi6gciYiIiFxE5UhERETkIipHIiIiIhdRORIRERG5iMqRiIiIyEVUjkREREQu8v+HBlQdm9MUJAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n",
      "Code test passed\n",
      "Go on to the next step\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "xmin = -10\n",
    "xmax = 10\n",
    "ymin = -10\n",
    "ymax = 10\n",
    "points = 2*(xmax-xmin)\n",
    "\n",
    "# Define the x values once\n",
    "x = np.linspace(xmin,xmax,points)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "plt.axis([xmin,xmax,ymin,ymax]) # window size\n",
    "plt.plot([xmin,xmax],[0,0],'b') # blue x axis\n",
    "plt.plot([0,0],[ymin,ymax], 'b') # blue y axis\n",
    "\n",
    "# line 1\n",
    "y1 = 2*x\n",
    "plt.plot(x, y1)\n",
    "\n",
    "# line 2\n",
    "y2 = -x - 3\n",
    "plt.plot(x, y2)\n",
    "\n",
    "plt.show()\n",
    "\n",
    "\n",
    "# Only change code above this line\n",
    "import math_code_test_b as test\n",
    "test.step11(In[-1].split('# Only change code above this line')[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ykj42UNeF7K5"
   },
   "source": [
    "# Step 12 - Systems of Equations - Algebra"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "n_-rpo6nF7K7"
   },
   "source": [
    "In a system of equations, the solution is the point where the two equations intersect, the (x,y) values that work in each equation. To work with algabraic expressions, you will import `sympy` and define x and y as symbols. If you have two equations and two variables, set each equation equal to zero. The `linsolve()` function takes the non-zero side of each equation and the variables used. Notice the syntax. Run the code, then change the two equations to solve 2x + y - 15 = 0 and 3x - y = 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "id": "6dFzZfqRF7K7",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{(3, 9)}\n",
      " \n",
      "Code test passed\n",
      "Go on to the next step\n"
     ]
    }
   ],
   "source": [
    "from sympy import *\n",
    "x,y = symbols('x y')\n",
    "\n",
    "\n",
    "# Change the equations in the following line: \n",
    "print(linsolve([2*x + y - 15, 3*x - y], (x, y)))\n",
    "\n",
    "\n",
    "# Only change code above this line\n",
    "import math_code_test_b as test\n",
    "test.step12(In[-1].split('# Only change code above this line')[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "QSKeBTgXHRAv"
   },
   "source": [
    "# Step 13 - Solutions as Coordinates"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "D2Ca3L-fHCzi"
   },
   "source": [
    "The `linsolve()` function returns a <i>finite set</i>, and you can convert that \"finite set\" into (x,y) coordinates. Notice how the code parses the `solution` variable into two separate variables. Just run the code to see how this works."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "id": "7uhBD85SHK3S",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x =  0\n",
      "y =  0\n",
      " \n",
      "Solution: ( 0 , 0 )\n",
      "Code test Passed\n",
      "Go on to the next step\n"
     ]
    }
   ],
   "source": [
    "from sympy import *\n",
    "x,y = symbols('x y')\n",
    "\n",
    "# Use variables for each equation\n",
    "first = x + y\n",
    "second = x - y\n",
    "\n",
    "# parse finite set answer as coordinate pair\n",
    "solution = linsolve([first, second], (x, y))\n",
    "x_solution = solution.args[0][0]\n",
    "y_solution = solution.args[0][1]\n",
    "\n",
    "print(\"x = \", x_solution)\n",
    "print(\"y = \", y_solution)\n",
    "print(\" \")\n",
    "print(\"Solution: (\",x_solution,\",\",y_solution,\")\") # remember this syntax\n",
    "\n",
    "\n",
    "# Just run this code\n",
    "import math_code_test_b as test\n",
    "test.step01()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "0epVLhL0F88U"
   },
   "source": [
    "# Step 14 - Systems from User Input"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "VhoI5uNrF88V"
   },
   "source": [
    "For more flexibility, you can get each equation as user input (instead of defining them in the code). Run this code and try it out - to solve any system of two equations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "id": "8irtXhucF88W",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Remember to use Python syntax with x and y as variables\n",
      "Notice how each equation is already set equal to zero\n"
     ]
    },
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      "Enter the first equation: 0 =  2*x + 3*y\n",
      "Enter the second equation: 0 =  4 + x - 2*y\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x =  -12/7\n",
      "y =  8/7\n",
      " \n",
      "If you didn't get a syntax error, code test passed\n"
     ]
    }
   ],
   "source": [
    "from sympy import *\n",
    "\n",
    "x,y = symbols('x y')\n",
    "print(\"Remember to use Python syntax with x and y as variables\")\n",
    "print(\"Notice how each equation is already set equal to zero\")\n",
    "first = input(\"Enter the first equation: 0 = \")\n",
    "second = input(\"Enter the second equation: 0 = \")\n",
    "solution = linsolve([first, second], (x, y))\n",
    "# remember this syntax\n",
    "x_solution = solution.args[0][0]\n",
    "y_solution = solution.args[0][1]\n",
    "\n",
    "print(\"x = \", x_solution)\n",
    "print(\"y = \", y_solution)\n",
    "\n",
    "\n",
    "# Just run this code and test it with different equations\n",
    "import math_code_test_b as test\n",
    "test.step14()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "8FCFQaq1Hizh"
   },
   "source": [
    "# Step 15 - Solve and graph a system"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "wMwKLQvyHaWp"
   },
   "source": [
    "Now you can put it all together: solve a system of equations, graph the system, and plot a point where the two lines intersect. Notice how this code is not like the previous solving equations code or the graphing code or the user input code. Python uses `sympy` to get the (x,y) solution and `numpy` to get the values to graph, so the user inputs nummerical values and the code uses them in two different ways. Think about how you would do this if the user input values for ax + by = c."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "id": "wLBNm5j6HffY",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "First equation: y = mx + b\n"
     ]
    },
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      "Enter m and b, separated by a comma:  2, 3\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Second equation: y = mx + b\n"
     ]
    },
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      "Enter m and b, separated by a comma:  1, 2\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n",
      "Solution: ( -1.0 , 1.0 )\n"
     ]
    }
   ],
   "source": [
    "from sympy import *\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "print(\"First equation: y = mx + b\")\n",
    "mb_1 = input(\"Enter m and b, separated by a comma: \")\n",
    "mb_in1 = mb_1.split(\",\") # split the value into two part\n",
    "m1 = float(mb_in1[0])\n",
    "b1 = float(mb_in1[1])\n",
    "\n",
    "print(\"Second equation: y = mx + b\")\n",
    "mb_2 = input(\"Enter m and b, separated by a comma: \")\n",
    "mb_in2 = mb_2.split(\",\")\n",
    "m2 = float(mb_in2[0])\n",
    "b2 = float(mb_in2[1])\n",
    "\n",
    "# Solve the system of equations\n",
    "x,y = symbols('x y')\n",
    "first = m1*x + b1 - y\n",
    "second = m2*x + b2 - y \n",
    "solution = linsolve([first, second], (x, y))\n",
    "x_solution = round(float(solution.args[0][0]),3)\n",
    "y_solution = round(float(solution.args[0][1]),3)\n",
    "\n",
    "# Make sure the window includes the solution\n",
    "xmin = int(x_solution) - 20\n",
    "xmax = int(x_solution) + 20\n",
    "ymin = int(y_solution) - 20\n",
    "ymax = int(y_solution) + 20\n",
    "points = 2*(xmax-xmin)\n",
    "\n",
    "# Define the x values once for the graph\n",
    "graph_x = np.linspace(xmin,xmax,points)\n",
    "\n",
    "# Define the y values for the graph\n",
    "y1 = m1*graph_x + b1\n",
    "y2 = m2*graph_x + b2\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "plt.axis([xmin,xmax,ymin,ymax]) # window size\n",
    "plt.plot([xmin,xmax],[0,0],'b') # blue x axis\n",
    "plt.plot([0,0],[ymin,ymax], 'b') # blue y axis\n",
    "\n",
    "# line 1\n",
    "plt.plot(graph_x, y1)\n",
    "\n",
    "# line 2\n",
    "plt.plot(graph_x, y2)\n",
    "\n",
    "# point\n",
    "plt.plot([x_solution],[y_solution],'ro')\n",
    "\n",
    "plt.show()\n",
    "print(\" \")\n",
    "print(\"Solution: (\", x_solution, \",\", y_solution, \")\")\n",
    "\n",
    "\n",
    "# Run this code and test it with different equations\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "BhKPZQJZF9w0"
   },
   "source": [
    "# Step 16 - Quadratic Functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "BYmD2FYHF9w1"
   },
   "source": [
    "Any function that involves x<sup>2</sup> is a \"quadratic\" function because \"x squared\" could be the area of a square. The graph is a parabola. The formula is y = ax<sup>2</sup> + bx + c, where `b` and `c` can be zero but `a` has to be a number. Here is a graph of the simplest parabola. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "id": "sfQl_A1CF9w1",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Code test Passed\n",
      "Go on to the next step\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "xmin = -10\n",
    "xmax = 10\n",
    "ymin = -10\n",
    "ymax = 10\n",
    "points = 2*(xmax-xmin)\n",
    "x = np.linspace(xmin,xmax,points)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "plt.axis([xmin,xmax,ymin,ymax]) # window size\n",
    "plt.plot([xmin,xmax],[0,0],'b') # blue x axis\n",
    "plt.plot([0,0],[ymin,ymax], 'b') # blue y axis\n",
    "\n",
    "y = x**2\n",
    "\n",
    "plt.plot(x,y)\n",
    "plt.show()\n",
    "\n",
    "# Just run this code. The next step will transform the graph\n",
    "import math_code_test_b as test\n",
    "test.step01()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "I0mklEluF-jI"
   },
   "source": [
    "# Step 17 - Quadratic Function ABC's"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "AJuHf8ySF-jJ"
   },
   "source": [
    "Using the parabola formula y = ax<sup>2</sup> + bx + c, you will change the values of `a`, `b`, and `c` to see how they affect the graph. Run the code and use the sliders to change the values of `a` and `b`. Then change the code in the three places indicated to add a slider for `c`. You may remember this type of interactive graph from an earlier step. Move each slider to see how it affects the graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "id": "9IVFnXxVF-jJ",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Code test passed\n",
      "Go on to the next step\n",
      " \n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a6437322bddb464ab2f032a9b8c8a6d0",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=0, description='a', max=9, min=-9), IntSlider(value=0, description='b', …"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from ipywidgets import interactive\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# Change the next line to include c:\n",
    "def f(a,b,c):\n",
    "    plt.axis([-10,10,-10,10]) # window size\n",
    "    plt.plot([-10,10],[0,0],'k') # blue x axis\n",
    "    plt.plot([0,0],[-10,10], 'k') # blue y axis\n",
    "    x = np.linspace(-10, 10, 1000)\n",
    "\n",
    "    # Change the next line to add c to the end of the function:\n",
    "    plt.plot(x, a*x**2 + b*x + c)\n",
    "    plt.show()\n",
    "\n",
    "# Change the next line to add a slider to change the c value\n",
    "interactive_plot = interactive(f, a=(-9, 9), b=(-9,9), c=(-9,9))\n",
    "interactive_plot\n",
    "\n",
    "\n",
    "# Run the code once, then change the code and run it again\n",
    "\n",
    "# Only change code above this line\n",
    "import math_code_test_b as test\n",
    "test.step17(In[-1].split('# Only change code above this line')[0])\n",
    "interactive_plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "eFehWNexGASC"
   },
   "source": [
    "# Step 18 - Quadratic Functions - Vertex"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "p8hAZw_CGASD"
   },
   "source": [
    "The <i>vertex</i> is the point where the parabola turns around. The x value of the vertex is $\\frac{-b}{2a}$ (and then you would calculate the y value to get the point). Write the code to find the vertex, given `a`, `b`, and `c` as inputs. Remember the parabola forumula is y = ax<sup>2</sup> + bx + c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "id": "cjMI5uZZGASD",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y = ax² + bx + c\n"
     ]
    },
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      "a =  2\n",
      "b =  1\n",
      "c =  4\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " ( -0.25  ,  3.875 )\n",
      " \n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n",
      "Code test passed\n",
      "Go on to the next step\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# \\u00b2 prints 2 as an exponent\n",
    "print(\"y = ax\\u00b2 + bx + c\")\n",
    "\n",
    "a = float(input(\"a = \"))\n",
    "b = float(input(\"b = \"))\n",
    "c = float(input(\"c = \"))\n",
    "\n",
    "# Write your code here, changing vx and vy\n",
    "vx = -b/(2*a)\n",
    "vy = a*vx**2 + b*vx + c\n",
    "\n",
    "\n",
    "# Only change the code above this line\n",
    "\n",
    "print(\" (\", vx, \" , \", vy, \")\")\n",
    "print(\" \")\n",
    "\n",
    "xmin = int(vx)-10\n",
    "xmax = int(vx)+10\n",
    "ymin = int(vy)-10\n",
    "ymax = int(vy)+10\n",
    "points = 2*(xmax-xmin)\n",
    "x = np.linspace(xmin,xmax,points)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "plt.axis([xmin,xmax,ymin,ymax]) # window size\n",
    "plt.plot([xmin,xmax],[0,0],'b') # blue x axis\n",
    "plt.plot([0,0],[ymin,ymax], 'b') # blue y axis\n",
    "\n",
    "plt.plot([vx],[vy],'ro') # vertex\n",
    "\n",
    "x = np.linspace(vx-10,vx+10,100) \n",
    "y = a*x**2 + b*x + c\n",
    "plt.plot(x,y)\n",
    "\n",
    "plt.show()\n",
    "\n",
    "\n",
    "# Only change code above this line\n",
    "import math_code_test_b as test\n",
    "test.step18(In[-1].split('# Only change code above this line')[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "WbqugasGGCKJ"
   },
   "source": [
    "# Step 19 - Projectile Motion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "TtM_pFHaGCKK"
   },
   "source": [
    "The path of every projectile is a parabola. For something thrown or launched upward, the `a` value is -4.9 (meters per second squared); the `b` value is the initial velocity (in meters per second); the `c` value is the initial height (in meters); the `x` value is time (in seconds); and the `y` value is the height at that time. In this code, change `vx` and `vy` to represent the vertex. Plotting that (x,y) vertex point is already in the code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "id": "FTNV_bjuGCKL",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      "Initial velocity =  5\n",
      "Initial height =  2\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " ( 0.5102040816326531 , 3.275510204081632 )\n",
      " \n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n",
      "Code test passed\n",
      "Go on to the next step\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "a = -4.9\n",
    "b = float(input(\"Initial velocity = \"))\n",
    "c = float(input(\"Initial height = \"))\n",
    "\n",
    "# Change vx and vy to represent the vertex\n",
    "vx = -b/(2*a)\n",
    "vy = a*vx**2 + b*vx + c\n",
    "\n",
    "\n",
    "# Also change the following dimensions to display the vertex\n",
    "xmin = -10\n",
    "xmax = 10\n",
    "ymin = -10\n",
    "ymax = 10\n",
    "\n",
    "# You do not need to change anything below this line\n",
    "points = 5*(xmax-xmin)\n",
    "x = np.linspace(xmin,xmax,points)\n",
    "y = a*x**2 + b*x + c\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "plt.axis([xmin,xmax,ymin,ymax]) # window size\n",
    "plt.plot([xmin,xmax],[0,0],'b') # blue x axis\n",
    "plt.plot([0,0],[ymin,ymax], 'b') # blue y axis\n",
    "\n",
    "plt.plot(x,y) # plot the line for the equation\n",
    "plt.plot([vx],[vy],'ro') # plot the vertex point\n",
    "\n",
    "print(\" (\", vx, \",\", vy, \")\")\n",
    "print(\" \")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "# Only change code above this line\n",
    "import math_code_test_b as test\n",
    "test.step19(In[-1].split('# Only change code above this line')[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "hN_fvENUGBAm"
   },
   "source": [
    "# Step 20 - Quadratic Functions - C"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "GrJNli5pGBAn"
   },
   "source": [
    "Like many other functions, the `c` value (also called the \"constant\" because it is not a variable) affects the vertical shift of the graph. Run the following code to see how changing the `c` value changes the graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "id": "hiSN0VexGBAn",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Code test Passed\n",
      "Go on to the next step\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import time\n",
    "from IPython import display\n",
    "\n",
    "x = np.linspace(-4,4,16) \n",
    "fig, ax = plt.subplots()\n",
    "cvalue = \"c = \"\n",
    "\n",
    "for c in range(10):\n",
    "    y = -x**2+c\n",
    "    plt.plot(x,y)\n",
    "    cvalue = \"c = \", c\n",
    "    ax.set_title(cvalue)\n",
    "    display.display(plt.gcf())\n",
    "    time.sleep(0.5)\n",
    "    display.clear_output(wait=True)\n",
    "\n",
    "# Just run this code\n",
    "import math_code_test_b as test\n",
    "test.step01()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "vteEy9QFGD5I"
   },
   "source": [
    "# Step 21 - The Quadratic Formula"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "xALyhEsNGD5J"
   },
   "source": [
    "For a projectile, you also need to find the point when it hits the ground. On a graph, you would call these points the \"roots\" or \"x intercepts\" or \"zeros\" (because y = 0 at these points). The <i>quadratic formula</i> gives you the x value when y = 0. Given `a`,`b` and `c`, here is the quadratic formula:<br> x = $\\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}$ Notice it's the vertex plus or minus something: $\\frac{-b}{2a} + \\frac{\\sqrt{b^2 - 4ac}}{2a}$ and $\\frac{-b}{2a} - \\frac{\\sqrt{b^2 - 4ac}}{2a}$ <br>\n",
    "Write the code to output two x values, given a, b, and c as input. Use `math.sqrt()` for the square root."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "id": "R3OIh1pOGD5K",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 = ax² + bx + c\n"
     ]
    },
    {
     "name": "stdin",
     "output_type": "stream",
     "text": [
      "a =  2\n",
      "b =  5\n",
      "c =  1\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The roots are  -0.21922359359558485  and  -2.2807764064044154\n",
      " \n",
      "Code test passed\n",
      "Go on to the next step\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "# \\u00b2 prints 2 as an exponent\n",
    "print(\"0 = ax\\u00b2 + bx + c\")\n",
    "a = float(input(\"a = \"))\n",
    "b = float(input(\"b = \"))\n",
    "c = float(input(\"c = \"))\n",
    "x1 = 0\n",
    "x2 = 0\n",
    "\n",
    "# Check for non-real answers:\n",
    "if b**2-4*a*c < 0:\n",
    "    print(\"No real roots\")\n",
    "else:\n",
    "    # Write your code here, changing x1 and x2\n",
    "    x1 = (-b+math.sqrt(b**2-4*a*c))/(2*a)\n",
    "    x2 = (-b-math.sqrt(b**2-4*a*c))/(2*a)\n",
    "    print(\"The roots are \", x1, \" and \", x2)\n",
    "\n",
    "\n",
    "\n",
    "# Only change code above this line\n",
    "import math_code_test_b as test\n",
    "test.step21(In[-1].split('# Only change code above this line')[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "VXxx7RCVSs4j"
   },
   "source": [
    "# Step 22 - Table of Values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "9Bd8bgPISiRH"
   },
   "source": [
    "In addition to graphing a function, you may need a table of values. This code shows how to make a simple table of (x,y) values. Run the code, then change the title to \"y = 3x + 2\" and change the function in the table. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "id": "e4dBSioJGGd3",
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " \n",
      "Code test passed\n",
      "Go on to the next step\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "ax = plt.subplot()\n",
    "ax.set_axis_off()\n",
    "title = \"y = 3x + 2\" # Change this title\n",
    "cols = ('x', 'y')\n",
    "rows = []\n",
    "for a in range(1,10):\n",
    "    rows.append([a, 3*a+2]) # Change only the function in this line\n",
    "    \n",
    "ax.set_title(title) \n",
    "plt.table(cellText=rows, colLabels=cols, cellLoc='center', loc='upper left')\n",
    "plt.show()\n",
    "\n",
    "\n",
    "# Only change code above this line\n",
    "import math_code_test_b as test\n",
    "test.step22(In[-1].split('# Only change code above this line')[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "jpo7oASHGEu7"
   },
   "source": [
    "# Step 23 - Projectile Game"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "WHx9faGkGEu7"
   },
   "source": [
    "Learn quadratic functions by building a projectile game. Starting at (0,0) you launch a toy rocket that must clear a wall. You can randomize the height and location of the wall. The goal is to determine what initial velocity would get the rocket over the wall. Bonus: make an animation of the path of the rocket.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "-yFfSgoeWHN3",
    "tags": []
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "pE5o0-VMaIy3"
   },
   "source": [
    "# Step 24 - Define Graphing Functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "c5tXoITnag_P"
   },
   "source": [
    "Building on what you have already done, create a menu with the following options:<br>\n",
    "<ul>\n",
    "<li>Display the graph and a table of values for any \"y=\" equation input</li>\n",
    "<li>Solve a system of two equations without graphing</li>\n",
    "<li>Graph two equations and plot the point of intersection</li>\n",
    "<li>Given a, b and c in a quadratic equation, plot the roots and vertex</li>\n",
    "</ul>\n",
    "Then think about how you will define a function for each item."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "lvuStaKYalPo"
   },
   "outputs": [],
   "source": [
    "# Write your code here\n",
    "\n",
    "\n",
    "# This step does not have a test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "D7ASvHg3b2Ph"
   },
   "source": [
    "# Step 25 - Certification Project 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "KBcTUf08cRy1"
   },
   "source": [
    "Build a graphing calculator that performs the functions mentioned in the previous step:\n",
    "<ul>\n",
    "<li>Display the graph and a table of values for any \"y=\" equation input</li>\n",
    "<li>Solve a system of two equations without graphing</li>\n",
    "<li>Graph two equations and plot the point of intersection</li>\n",
    "<li>Given a, b and c in a quadratic equation, plot the roots and vertex</li>\n",
    "</ul>\n",
    "Define each of the functions, and make each option call a function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "bmuz1zCecVCX"
   },
   "outputs": [],
   "source": [
    "# Write your code here\n",
    "\n",
    "\n",
    "# This step does not have a test"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "authorship_tag": "ABX9TyMgIJXFt8DsKZCyvmAbfh4p",
   "collapsed_sections": [
    "szp5flp1fA8-",
    "iNcDJ45bGtYk",
    "ZWDxpIPUFfda",
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