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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