# GRAPHING WITH INTERCEPTS

## About "Graphing with intercepts"

Graphing with intercepts :

Whenever we want to graph a line using intercepts, we can use one of the following methods to find x and y-intercepts.

(i) By comparing the given equation into intercept form and find x and y-intercepts.

(ii) Another way is to find x intercept we have to put y = 0. To find y-intercept we have to put x = 0.

Let us see some example problems to understand the above methods.

## Graphing with intercepts - Examples

Example 1 :

Graph the given line using intercepts.

2x + 3y = 12

Solution :

Method 1 :

Compare the given equation with intercept form

(x/a) + (y/b) = 1

In order to compare, we have to divide the whole equation by 12.

(2x/12) + (3y/12) = 12/12

(x/6) + (y/4) = 1

x-intercept (a) = 6

y-intercept (b) = 4

Method 2 :

To find x-intercept, we have to put y = 0

2x + 3y = 12

2x + 3(0) = 12 ==> 2x + 0 = 12 ==> 2x = 12

Divide by 2 on both sides, we get

x = 6

To find y-intercept, we have to put x = 0

2(0) + 3y = 12 ==> 3y = 12

Divide by 3 on both sides, we get

y = 4

Hence x and y intercepts are 6 and 4 respectively.

So we have to plot the points (6,0) and (0,4) and draw the line which connects the above points. Example 2 :

Graph the given line using intercepts.

5x + y - 10 = 0

Solution :

Method 1 :

Compare the given equation with intercept form

(x/a) + (y/b) = 1

In order to compare, add by 10 on both sides

5x - y - 10 = 0 + 10

5x - y = 10

divide by 10 on both sides

(5x/10) - (y/10) = (10/10)

x/2 + y/(-10) = 1

x-intercept (a) = 2

y-intercept (b) = -10

Method 2 :

To find x-intercept, we have to put y = 0

5x - y - 10 = 0

5x - 0 - 10 = 0 ==> 5x = 10

Divide by 5 on both sides, we get

x = 2

To find y-intercept, we have to put x = 0

5(0) - y - 10 ==> -y - 10 = 0

Add 10 on both sides

-y = 10 ==> y = -10

Hence x and y intercepts are 2 and -10 respectively.

So we have to plot the points (2,0) and (0,-10) and draw the line which connects the above points. Example 3 :

Graph the given line using intercepts.

y = 4x - 4

Solution :

Method 1 :

Compare the given equation with intercept form

(x/a) + (y/b) = 1

y = 4x - 4

Subtract y on both sides

y - y = 4x - y - 4

0 = 4x - y - 4

Add by 4 on both sides

4x - y = 4

Divide by 4 on both sides

(4x/4) - (y/4) = (4/4)

[x/1] + [y/(-4)] = 1

x-intercept (a) = 1

y-intercept (b) = -4

Method 2 :

To find x-intercept, we have to put y = 0

y = 4x - 4

4x - 4 = 0 ==> 4x = 4

Divide by 4 on both sides, we get

x = 1

To find y-intercept, we have to put x = 0

y = 4(0) - 4 ==> y = -4

Hence x and y intercepts are 1 and -4 respectively.

So we have to plot the points (1,0) and (0,-4) and draw the line which connects the above points. Example 4 :

Graph the given line using intercepts.

y = -x/2 - 2

Solution :

x-intercept, put y = 0

0 = (-x/2) - 2

Add 2 on both sides

2 = -x/2

Multiply 2 on both sides

4 = -x ==> x  = -4

y-intercept, put x = 0

y = (-0/2) - 2

y = -2

Hence x and y-intercepts are -4 and -2

So we have to plot the points (-4,0) and (0,-2) and draw the line which connects the above points. After having gone through the stuff given above, we hope that the students would have understood "Graphing with intercepts".

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