Math Guide

GraphingNon Linear equations

A set of equations which are dealt withall together is called system of equations. They consist of more thanone equation at one time. There are two types of equations, linearequations and non-linear equations. Linear equations are theequations whose graph would be a straight line (linear). Non-linearequation graph does not result in a straight line.


The degree of the variables is eitherless than one or more than one, but never equal to one. Though theuniqueness of solutions is more complicated than for linearequations, they can have any number of solutions.


Examplesof Non Linear Equations are: the system of equations y="x2and y="8-x2; y="-x2+6 and y="-2x-2;" x3+6x2+11x-6


Let us now learn thesteps involved in Graphing Non Linearequations. The graph of a non linear equation in twovariables would not necessarily be a straight line. The stepsinvolved in graphing are as follows:


  • First the points that satisfy theequation are calculated

  • The points are plotted on thegraph

  • Once enoughpoints are plotted to determine the graph, the graph is drawn. Ifthere are not enough points then get more points using the firststep


Sufficiently manypoints must be plotted to get the proper graph, usually more thanthree points are required. Let us consider an example, graph thenon-linear equation y="2-x2


Step1: First thepoints that satisfy the equation y="4-x2 are calculated andtabulated

Let us consider 7values of x as follows,

Whenx = -3, y="4" - (-3)2= 4-9= -5

x = -2,y="4" - (-2)2= 4-4= 0

x = -1,y="4" – (-1)2 = 4 – 1="3

x = 0, y= 4 – (0)2= 4 – 0 = 4

x = 1, y= 4 – (1)2= 4 – 1 = 3

x = 2, y= 4 – (2)2 = 4 – 4 = 0

x = 3, y= 4 – (3)2 = 4 – 9 = -5

Tabulating theabove values we get,

x -3-2 -10 1 2 3

y -5 0 3 4 3 0 -5

So thepoints are: (x, y)=(-3,-5),(-2,0), (-1,3), (0,4), (1,3), (2,0),(3,-5)


Step2: The abovepoints are plotted on the graph