Math Guide

GraphingLinear Equations

Equations whosegraph is a straight line extending on both sides are called linearequations. Linear straight andhence the equation is a straight line. The equation would be in twovariables x and y which is written in the form y="mx+b" where ‘m’is the slope of the line and ‘b’ is the intercept of y-axis.


Slope is the ratioof the change in y values (rise) to the change in the x values (run);slope m="rise/run." The y-intercept is the point where the straightline cuts the y-axis (y=b). Graphing LinearEquations involves a very simple process.


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The steps are asfollows:


  • First thex-axis and y-axis are drawn perpendicular on a graph paper. Thevertical line being the y-axis and the horizontal line being thex-axis. The point of intersection of these two axes is the origin(0,0)

  • The givenlinear equation has be in the form y="mx+b," if not re-write theequation to the slope-intercept form

  • Draw a T-chartwhich consists of two columns, x values, y values [a third column isoptional for the coordinates (x,y)]

  • The x-valueswould be the different values chosen which are plugged into thegiven equation to arrive to the respective y-values

  • To plot a graphthe minimum number of points required is three. Once the coordinatesare determined they are plotted on the graph

  • The points arejoined to give a straight line, it cuts the y-axis at y="b

  • The lineextends on both sides which is shown with arrow marks on eitherside, this line represents the given equation


Let us now considera simple example to learn how to graphlinear equation. Graph the equation given by, y="3x-2


First we choosedifferent x-values and plug in the values in the given equation forthe various y-values. We shall consider five values of x and draw aT-chart as follows


x y="3x-2"(x,y)

-2 y="3(-2)-2=-8" (-2,-8)

-1 y="3(-1)-2=-5" (-1,-5)

0 y="3(0)" –2="-2" ( 0, -2)

1 y="3(1)" – 2="1" ( 1, 1)

2 y="3(2)" –2="4" (2, 4)

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


Now that the pointsare determined, two perpendicular lines are drawn on a graph paperwhich represents the x-axis and the y-axis respectively. Thecoordinate points are plotted and joined.


The straight lineformed is the required graph of the given equation. Thus we can plota linear graph of the givenstraight equation. The graph of the above given equation is asfollows,