# GRAPHING LINEAR EQUATIONS USING INTERCEPTS

## About "Graphing linear equations using intercepts"

Graphing linear equations using intercepts :

In this section, we are going to see, how linear equations can be graphed using intercepts.

## Graphing linear equations using intercepts - Steps

The linear equation may be given in any form.(General form, Slope intercept form, Intercepts form, etc.,)

We have to do the following steps to graph a linear equation which may be given in any of the above forms.

Step 1 :

Finding x - intercept.

Substitute y  =  0 in the given linear equation to find x - intercept.

For example, if you get x-intercept "a" (That is x = a), write this as a point (a, 0).

Step 2 :

Finding y - intercept.

Substitute x  =  0 in the given linear equation to find y - intercept.

For example, if you get y-intercept "b" (That is y = b), write this as a point (0, b).

Step 3 :

Plot the points (a, 0) and (0, b) in xy-plane and connect them to get the graph (straight line) of the given linear equation.

## Graphing linear equations using intercepts - Examples

Example 1 :

Graph the linear equation 2x - 3y + 6 = 0 using intercepts.

Solution :

Step 1 :

Find x-intercept.

Substitute y = 0 in the given equation.

2x - 3(0) + 6  =  0

2x + 6  =  0

Subtract 6 from both sides.

(2x + 6) - 6  =  0 - 6

2x  =  -6

Divide both sides by 2.

(2x)/2  =  -6/2

x  =  -3

The point corresponding to the x-intercept "-3" is (-3, 0).

Step 2 :

Find y-intercept.

Substitute x = 0 in the given equation.

2(0) - 3y + 6  =  0

-3y + 6  =  0

Subtract 6 from both sides.

(-3y + 6) - 6  =  0 - 6

-3y  =  -6

Divide both sides by -3.

(-3y)/(-3)  =  (-6)/(-3)

y  =  2

The point corresponding to the y-intercept "2" is (0, 2).

Step 3 :

Plot the two points (-3, 0) and (0, 2) in xy-plane and connect them to get the graph of the equation 2x - 3y + 6 = 0.

Example 2 :

Graph the linear equation y =  (2/3)x - 4 using intercepts.

Solution :

Step 1 :

Find x-intercept.

Substitute y = 0 in the given equation.

0  =  (2/3)x - 4

0 + 4   =  [(2/3)x - 4] + 4

4  =  (2/3)x

Multiply both sides by 3/2.

(4)(3/2)  =  [(2/3)x](3/2)

6  =  x

The point corresponding to the x-intercept "6" is (6, 0).

Step 2 :

Find y-intercept.

Substitute x = 0 in the given equation.

y  =  (2/3)(0) - 4

y   =  - 4

The point corresponding to the y-intercept "-4" is (0, -4).

Step 3 :

Plot the two points (6, 0) and (0, -4) in xy-plane and connect them to get the graph of the equation y =  (2/3)x - 4.

After having gone through the stuff given above, we hope that the students would have understood "How to graph linear equations using intercepts".

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