{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 9 The Law of Straight Line and Co ordinates"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 9_1 pgno:99"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "the number is  230\n"
     ]
    },
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa77a6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#let a-the avg. amount paid. x-no. of customers.  b-the expenses\n",
    "#net profit is y=ax-b\n",
    "x=320;y=4.50;\n",
    "x=250;y=1.00;\n",
    "#substitute in above equation\n",
    "import numpy\n",
    "import matplotlib\n",
    "from matplotlib import pyplot\n",
    "%matplotlib inline\n",
    "\n",
    "#4.5=320*a-b-equ.1;1=250*a-b-equ.2.subbstract equ.2 from 1.\n",
    "a=0.05;#we get\n",
    "b=250*a-1;\n",
    "\n",
    "#x is a polynomial function of degree zerox=poly(0,'x');\n",
    "#y=numpy.array[(0.05, -11.5)];#equation to straight line\n",
    "#if there is no profit i.e., y=0\n",
    "\n",
    "x=0;\n",
    "for x in range(0,500):\n",
    "  if(0.05*x-11.5==0):\n",
    "    print\"the number is \",x \n",
    "\t\n",
    "\n",
    "\n",
    "cust=numpy.array([230, 240, 270, 300, 350, 380]);\n",
    "profit=numpy.array([0, 0.5, 2.0, 3.5, 6.0, 7.5]);\n",
    "pyplot.plot(cust,profit);\n",
    "pyplot.plot(230,0);\n",
    "#profit(y) depends on varying no. of customers(x). the no.'s 0.05 & 11.5 remained constant\n",
    "pyplot.title(\"the straight line graph\"),\n",
    "pyplot.xlabel(\"no. of customers\")\n",
    "pyplot.ylabel(\"profit\");\n",
    "pyplot.legend(\"y=0.05*x-11.5\");\n",
    "pyplot.grid()\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 9_2 pgno:103"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-2  0  1  3  5  5]\n"
     ]
    },
    {
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       "1wqdLWQlCDUAAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0xab70128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#2*y-4*x=3\n",
    "import numpy\n",
    "import matplotlib\n",
    "from matplotlib import pyplot\n",
    "%matplotlib inline\n",
    "#x is a polynomial function of degree zero  x=#poly(0,'x');\n",
    "x=numpy.array([-2., -1., 0, 1., 1.8, 2.]);\n",
    "y=numpy.array([0, 0, 0, 0, 0, 0]);\n",
    "i=0;\n",
    "for i in range (0,6):\n",
    "\ty[i]=(3.+4.*x[i])/2.;\n",
    "\ti=i+1\n",
    "print y\n",
    "y=numpy.array([-2.5, -0.5, 1.5, 3.5, 5.1, 5.5])\n",
    "pyplot.plot(x,y)\n",
    "pyplot.plot(0,1.5,'o')#when x=0. 1.5 is intercept on y-axis\n",
    "pyplot.plot(-0.75,0,'o')#when y=0. -0.75 is intercept on x-axis\n",
    "pyplot.title('graph of equation 2y-4x-3')\n",
    "pyplot.xlabel('x axis')\n",
    "pyplot.ylabel('y axis')\n",
    "pyplot.grid()\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 9_3 pgno:104"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 5  3  1 -1 -3 -5]\n"
     ]
    },
    {
     "data": {
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       "QmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x3e9cc88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy\n",
    "import matplotlib\n",
    "from matplotlib import pyplot\n",
    "%matplotlib inline\n",
    "#x is a polynomial function of degree zero  x=#poly(0,'x');\n",
    "x=numpy.array([-2, -1, 0, 1, 2, 3]);\n",
    "y=numpy.array([0, 0, 0, 0, 0, 0]);\n",
    "i=0;\n",
    "for i in range (0,6):\n",
    "\ty[i]=(1-2*x[i]);\n",
    "\ti=i+1\n",
    "print y\n",
    "\n",
    "pyplot.plot(x,y)\n",
    "pyplot.plot(0,1,'o')#when x=0. 1.5 is intercept on y-axis\n",
    "pyplot.plot(0.5,0,'o')#when y=0. -0.75 is intercept on x-axis\n",
    "pyplot.title('graph of equation 2y-4x-3')\n",
    "pyplot.xlabel('x axis')\n",
    "pyplot.ylabel('y axis')\n",
    "pyplot.grid()\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 9_4 pgno:112"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ex(1) In y=4x-7, gradient is 4.Intercept on y-axis is -7\n",
      "ex(2) In y=0.05x-11.5, gradient is 0.05 and intercept on y-axis is -11.5\n"
     ]
    },
    {
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       "zMwAJwQzM8s5IZiZGeCEYGZmOScEMzMD4P8DtzEwevQUUb0AAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0xab7a128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "#y=mx+b\n",
    "import numpy\n",
    "import matplotlib\n",
    "from matplotlib import pyplot\n",
    "%matplotlib inline\n",
    "\n",
    "x=numpy.array([0, 1, 2, 3]);\n",
    "y=x;\n",
    "pyplot.plot(x,y);\n",
    "y=x+2;\n",
    "pyplot.plot(x,y);\n",
    "y=x-3;\n",
    "pyplot.plot(x,y);\n",
    "pyplot.title(\"Equations of the form y=mx+b\")\n",
    "pyplot.xlabel(\"x axis\")\n",
    "pyplot.ylabel(\"y axis\");\n",
    "pyplot.legend(\"y=x\")\n",
    "pyplot.legend(\"y=x+2\")\n",
    "pyplot.legend(\"y=x-3\")\n",
    "pyplot.grid()\n",
    "#m is constant, b is fixed distance. (x,y) vary for different points on the line \n",
    "\n",
    "#ex(1)\n",
    "print\"ex(1) In y=4x-7, gradient is 4.Intercept on y-axis is -7\"\n",
    "#ex(2)\n",
    "print\"ex(2) In y=0.05x-11.5, gradient is 0.05 and intercept on y-axis is -11.5\"\n",
    "pyplot.show()\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 9_5 pgno:114"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2 3 1 0]\n",
      "[-3.5    -5.     -2.1875  2.5   ]\n",
      "the solution of the equation is\n",
      "x=\n",
      "y=  3 1\n"
     ]
    },
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa7e1f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy\n",
    "import matplotlib\n",
    "from matplotlib import pyplot\n",
    "%matplotlib inline\n",
    "#x is a polynomial function of degree zero  x=#poly(0,'x');\n",
    "#graph of x+2*y=5\n",
    "x=numpy.array([0, -1, 2, 5]);\n",
    "y=numpy.array([0, 0, 0, 0]);\n",
    "i=0;\n",
    "for i in range (0,3):\n",
    "\ty[i]=(5-x[i])/2;\n",
    "\ti=i+1\n",
    "print y\n",
    "y=numpy.array([2.5, 3, 1.5, 0])\n",
    "pyplot.plot(x,y);\n",
    "#graph of 3*x-2*y=7\n",
    "x=numpy.array([0, -1, 7./8., 4]);\n",
    "y=numpy.array([0, 0, 0, 0]);\n",
    "y=(3*x-7)/2;\n",
    "\n",
    "for i in range (0,3):\n",
    "\ty[i]=(3*x[i]-7)/2;\n",
    "\ti=i+1\n",
    "print y\n",
    "y=numpy.array([-3.5, -5, -2.1875, 2.5 ])\n",
    "pyplot.plot(x,y)\n",
    "for x in range(1,100):\n",
    "  if((5-x)/2==(3*x-7)/2):\n",
    "    break\n",
    "\n",
    "print\"the solution of the equation is\"\n",
    "y=(5-x)/2;\n",
    "print\"x=\\ny= \",x,y\n",
    "pyplot.plot(x,y)\n",
    "\n",
    "\n",
    "pyplot.plot(x,y)\n",
    "pyplot.plot(1,3,'x')#when x=0. 1.5 is intercept on y-axis\n",
    "pyplot.plot(0.5,0,'o')#when y=0. -0.75 is intercept on x-axis\n",
    "pyplot.title('graph of equation 2y-4x-3')\n",
    "pyplot.xlabel('x axis')\n",
    "pyplot.ylabel('y axis')\n",
    "#pyplot.legend(\"x+2*y=5\",\"3*x-2*y=7\");\n",
    "\n",
    "pyplot.grid()\n",
    "pyplot.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}