**GraphingLinear Equations**

**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,