# FIND X AND Y INTERCEPTS

## About "Find x and y intercepts"

Find x and y intercepts :

X-intercept :

The x-intercept is where a line crosses the x-axis. To find the x-intercept, we have to put y = 0 and solve the value for x.

Y-intercept :

The y-intercept is the point where the line crosses the y-axis. To find the y-intercept, we have to put x = 0 and solve the value for y.

Example 1 :

Find the x and y intercepts of the following equation.

2x + 3y = 12

Solution :

X-intercept :

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

Y-intercept :

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 :

Find the x and y intercepts of the following equation.

5x + y - 10 = 0

Solution :

X-intercept :

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

Y-intercept :

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 :

Find the x and y intercepts of the following equation.

y = 4x - 4

Solution :

X-intercept :

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

Y-intercept :

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 :

Find the x and y intercepts of the following equation.

y = -x/2 - 2

Solution :

X-intercept :

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 :

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.

Example 5 :

Find the x intercepts of the following parabola.

y = x² - 3 x

Solution :

X-intercept :

x-intercept, put y = 0

0 = x² - 3 x

x² - 3 x = 0

x (x - 3) = 0

x = 0        x - 3 = 0

x = 3

After having gone through the stuff given above, we hope that the students would have understood "Find x and y intercepts".

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