Intercepts of lines review (x-intercepts and y-intercepts)

The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. Thinking about intercepts helps us graph linear equations.

What are intercepts?

The xx-intercept is the point where a line crosses the xx-axis, and the yy-intercept is the point where a line crosses the yy-axis.
Want a deeper introduction to intercepts? Check out this video.

Example: Intercepts from a graph

Looking at the graph, we can find the intercepts.
The line crosses the axes at two points:
The point on the xx-axis is (5,0)(5,0). We call this the xx-intercept.
The point on the yy-axis is (0,4)(0,4). We call this the yy-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 xx and yy is linear.
xxyy
119-9
336-6
553-3
Then we're asked to find the intercepts of the corresponding graph.
The key is realizing that the xx-intercept is the point where y=0y=0, and the yy-intercept is where x=0x=0.
The point (7,0)(7,0) is our xx-intercept because when y=0y=0, we're on the xx-axis.
To find the yy-intercept, we need to "zoom in" on the table to find where x=0x=0.
The point (0,10.5)(0,-10.5) is our yy-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=5
To find the yy-intercept, let's substitute x=0\blue x=\blue 0 into the equation and solve for yy:
30+2y=52y=5y=52\begin{aligned}3\cdot\blue{0}+2y&=5\\ 2y&=5\\ y&=\dfrac{5}{2}\end{aligned}
So the yy-intercept is (0,52)\left(0,\dfrac{5}{2}\right).
To find the xx-intercept, let's substitute y=0\pink y=\pink 0 into the equation and solve for xx:
3x+20=53x=5x=53\begin{aligned}3x+2\cdot\pink{0}&=5\\ 3x&=5\\ x&=\dfrac{5}{3}\end{aligned}
So the xx-intercept is (53,0)\left(\dfrac{5}{3},0\right).
Want to learn more about finding intercepts from equations? Check out this video.

Practice

Problem 1
Determine the intercepts of the line graphed below.
xx-intercept:
(\Big(
,,
)\Big)
yy-intercept:
(\Big(
,,
)\Big)
Want more practice? Check out these exercises:
Loading