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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 x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-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 x-axis is (5,0). We call this the x-intercept.
The point on the y-axis is (0,4). We call this the y-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 x and y is linear.
xy
19
36
53
Then we're asked to find the intercepts of the corresponding graph.
The key is realizing that the x-intercept is the point where y=0, and the y-intercept is where x=0.
The point (7,0) is our x-intercept because when y=0, we're on the x-axis.
To find the y-intercept, we need to "zoom in" on the table to find where x=0.
The point (0,10.5) is our y-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=5
To find the y-intercept, let's substitute x=0 into the equation and solve for y:
30+2y=52y=5y=52
So the y-intercept is (0,52).
To find the x-intercept, let's substitute y=0 into the equation and solve for x:
3x+20=53x=5x=53
So the x-intercept is (53,0).
Want to learn more about finding intercepts from equations? Check out this video.

Practice

Problem 1
Determine the intercepts of the line graphed below.
x-intercept:
(
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0.75
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
,
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0.75
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
)
y-intercept:
(
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0.75
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
,
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0.75
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
)

Want more practice? Check out these exercises: