**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=3x−10=3x−11=3×13=x(13,0)x-intercept\begin{array}{ll}y=3x – 1\qquad & \qquad \\ 0=3x – 1\qquad & \qquad \\ 1=3x\qquad & \qquad \\ \frac{1}{3}=x\qquad & \qquad \\ \left(\frac{1}{3},0\right)\qquad & x\text{-intercept}\qquad \end{array}

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=3x−1y=3(0)−1y=−1(0,−1)y-intercept\begin{array}{l}y=3x – 1\qquad \\ y=3\left(0\right)-1\qquad \\ y=-1\qquad \\ \left(0,-1\right)y\text{-intercept}\qquad \end{array}

y

=

3

x

−

1

y

=

3

(

0

)

−

1

y

=

−

1

(

0

,

−

1

)

y

-intercept

**Figure 12**

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

- Find the x-intercept by setting
y=0y=0

y

=

0

and solving for

xx

x

.

- Find the y-intercept by setting
x=0x=0

x

=

0

and solving for

yy

y

Read more : 3 Key Steps to a Concrete Floor Refresh

.

### 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=−3x−40=−3x−44=−3x−43=x(−43,0)x-intercept\begin{array}{l}y=-3x – 4\qquad \\ 0=-3x – 4\qquad \\ 4=-3x\qquad \\ -\frac{4}{3}=x\qquad \\ \left(-\frac{4}{3},0\right)x\text{-intercept}\qquad \end{array}

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=−3x−4y=−3(0)−4y=−4(0,−4)y-intercept\begin{array}{l}y=-3x – 4\qquad \\ y=-3\left(0\right)-4\qquad \\ y=-4\qquad \\ \left(0,-4\right)y\text{-intercept}\qquad \end{array}

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

Read more : How to Lower Your Electric Bill – NerdWallet

.

Solution

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

### Licenses and Attributions

#### CC licensed content, Specific attribution

- College Algebra.
**Authored by**: OpenStax College Algebra.**Provided by**: OpenStax.**Located at**: https://cnx.org/contents/ [ e-mail protected ]:1/Preface.

**License**: CC BY: Attribution

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