# Finding x-intercepts and y-intercepts

The intercepts of a graph constitute point at which the graph cross the axe. The x-intercept be the point at which the graph intersect the x-axis. at this point, the y-coordinate be zero. The y-intercept be the point at which the graph crisscross the y-axis. astatine this point, the x-coordinate embody zero.

To determine the x-intercept, we set y equal to zero and resolve for adam. similarly, to determine the y-intercept, we place ten equal to zero and clear for y. For example, get discover the intercept of the equality

y=3x−1y=3x – 1

y

=

3

x

1

.

To find the x-intercept, set

y=0y=0

y

=

0

.

y

=

3

x

1

0

=

3

x

1

1

=

3

x

3

1

=

x

(

3

1

,

0

)

x

-intercept

x=0x=0

x

=

0

.

y

=

3

x

1

y

=

3

(

0

)

1

y

=

1

(

0

,

1

)

y

-intercept Figure 12

### How To: Given an equation, find the intercepts.

1. Find the x-intercept by setting

y=0y=0

y

=

0

and solving for

xx

x

.

2. Find the y-intercept by setting

x=0x=0

x

=

0

and solving for

yy

y

.

### Example 4: Finding the Intercepts of the Given Equation

Find the intercepts of the equation

y=−3x−4y=-3x – 4

y

=

3

x

4

. Then sketch the graph using only the intercepts.

find oneself the wiretap of the equation. then cartoon the graph use only the intercept .

### Solution

Set

y=0y=0

y

=

0

to find the x-intercept.

y

=

3

x

4

0

=

3

x

4

4

=

3

x

3

4

=

x

(

3

4

,

0

)

x

-intercept

x=0x=0

x

=

0

to find the y-intercept.

y

=

3

x

4

y

=

3

(

0

)

4

y

=

4

(

0

,

4

)

y

-intercept Figure 13

Setto find the x-intercept.Setto discover the y-intercept.Plot both bespeak, and draw vitamin a line pass through them a in figure eleven .

### Try It 1

Find the intercepts of the equation and sketch the graph:

y=−34x+3y=-\frac{3}{4}x+3

y

=

4

3

x

+

3

.

Solution

find the wiretap of the equation and sketch the graph : solution