Math Guide

Graphinga Linear Equation in Two Variables

A linear function isthe one whose graph when plotted would be a straight line. The mostcommon form of linear function in two variables is y="mx+b," it isalso called the slope-intercept form. Linear means straight and hencethe graph of these functions is a straight line.

Here in thisequation x is an independent variable and y is the dependentvariable. Also the power of the variable x is always one and notgreater than one at any point. The coefficient ‘m’ of thevariable ‘x’ is the slope of the line which gives the rate ofchange of the dependent variable ‘x’ and b is the y-interceptthat is the point at which the line cuts the y-axis, it is the valueof the dependent variable y when x is zero.

So, the graphsof functions of two variables when different x values areconsidered would be a straight line.

The steps involvedin graphing a linear equation in twovariables are:

  • Consider minimum three values of x(minimum three points are required to plot a graph of a given linearequation)

  • Substitute each value of x in thegiven equation to arrive to the respective y-values

  • Tabulate the values of x and y

  • Plot all the (x,y) points on thegraph

  • Join the points to get a straightline, this line represents the given linear equation in twovariables

Let us consider an example tounderstand the steps involved in graphinglinear equations in two variables

Example: graph thelinear equation, y="3x-2

Solution: Givenequation, y="3x-2

First step would beto consider five x-values to make the plotting easier.

Let x="-2,-1,0,1,2

Next step would beto substitute each of these x-values in the given equation and arriveto the respective y-values

When x = -2, y=""3(-2) – 2="-6-2" = -8

When x="-1," y="3(-1)" –2 = -3-2= -5

When x="0," y="3(0)-2"= 0 – 2 = -2

When x="1," y="3(1)" –2 = 3 – 2 = 1

When x="2," y = 3(2) –2 = 6-2= 4

Now the above x andy values are tabulated

x -2 -1 0 1 2

y -8 -5 -2 1 4

The five points are,(x,y) = (-2,-8),(-1,-5), (0,-2), (1,1), (2,4)

These points areplotted on the graph and joined to get a straight line. The followingis the graph of y="3x-2" where 3 is the slope and -2 the y-intercept