Answer:
The xxx-intercept is the point where a line crosses the xxx-axis, and the yyy-intercept is the point where a line crosses the yyy-axis.
Explanation:
Looking at the graph, we can find the intercepts.
The line crosses the axes at two points:
The point on the xxx-axis is (5,0)(5,0)left parenthesis, 5, comma, 0, right parenthesis. We call this the xxx-intercept.
The point on the yyy-axis is (0,4)(0,4)left parenthesis, 0, comma, 4, right parenthesis. We call this the yyy-intercept.
Want to learn more about finding intercepts from graphs? Check out this video.
Example: Intercepts from a table
We're given a table of values and told that the relationship between xxx and yyy is linear.
xxx yyy
111 -9−9minus, 9
333 -6−6minus, 6
555 -3−3minus, 3
Then we're asked to find the intercepts of the corresponding graph.
The key is realizing that the xxx-intercept is the point where y=0y=0y, equals, 0, and the yyy-intercept is where x=0x=0x, equals, 0.
The point (7,0)(7,0)left parenthesis, 7, comma, 0, right parenthesis is our xxx-intercept because when y=0y=0y, equals, 0, we're on the xxx-axis.
To find the yyy-intercept, we need to "zoom in" on the table to find where x=0x=0x, equals, 0.
The point (0,-10.5)(0,−10.5)left parenthesis, 0, comma, minus, 10, point, 5, right parenthesis is our yyy-intercept.
Want to learn more about finding intercepts from tables? Check out this video.
Example: Intercepts from an equation
We're asked to determine the intercepts of the graph described by the following linear equation:
3x+2y=53x+2y=53, x, plus, 2, y, equals, 5
To find the yyy-intercept, let's substitute \blue x=\blue 0x=0start color #6495ed, x, end color #6495ed, equals, start color #6495ed, 0, end color #6495ed into the equation and solve for yyy:
\begin{aligned}3\cdot\blue{0}+2y&=5\\ 2y&=5\\ y&=\dfrac{5}{2}\end{aligned}
3⋅0+2y
2y
y
=5
=5
=
2
5
So the yyy-intercept is \left(0,\dfrac{5}{2}\right)(0,
2
5
)left parenthesis, 0, comma, start fraction, 5, divided by, 2, end fraction, right parenthesis.
To find the xxx-intercept, let's substitute \pink y=\pink 0y=0start color #ff00af, y, end color #ff00af, equals, start color #ff00af, 0, end color #ff00af into the equation and solve for xxx:
\begin{aligned}3x+2\cdot\pink{0}&=5\\ 3x&=5\\ x&=\dfrac{5}{3}\end{aligned}
3x+2⋅0
3x
x
=5
=5
=
3
5
So the xxx-intercept is \left(\dfrac{5}{3},0\right)(
3
5
,0)left parenthesis, start fraction, 5, divided by, 3, end fraction, comma, 0, right parenthesis.
Want to learn more about finding intercepts from equations? Check out this video.
Practice
PROBLEM 1
Determine the intercepts of the line graphed below.
xxx-intercept:
\Big((left parenthesis
,,comma
\Big))right parenthesis
yyy-intercept:
\Big((left parenthesis
,,comma
\Big))right parenthesis