y-intercept: y-coordinate of
the point where the graph
intersects the y-axis. The xcoordinate of this point is
always 0, i.e., (0, #).
x-intercept: x-coordinate of
the point where the graph
intersects the x-axis. The ycoordinate of this point is
always 0, i.e., (#, 0).
Example 1: Identifying Intercepts
Find the x- and y-intercepts.
The graph intersects the
y-axis at (0, 1).
The y-intercept is 1.
The graph intersects the
x-axis at (–2, 0).
The x-intercept is –2.
Example 2: Identifying Intercepts
Find the x- and y-intercepts.
The graph intersects the
y-axis at (0, -4).
The y-intercept is -4.
The graph intersects the
x-axis at (3, 0).
The x-intercept is 3.
Example 3: Identifying Intercepts
Find the x- and y-intercepts.
The graph intersects the
y-axis at (0, 3).
The y-intercept is 3.
The graph intersects the
x-axis at (–2, 0).
The x-intercept is –2.
Example 4: Finding Intercepts
Find the x- and y-intercepts.
5x – 2y = 10
To find the x-intercept,
replace y with 0 and solve
for x.
5x – 2y = 10
5x – 2(0) = 10
5x – 0 = 10
5x = 10
x=2
The x-intercept is 2.
5x – 2y = 10
5(0) – 2y = 10
0 – 2y = 10
– 2y = 10
y = –5
The y-intercept is –5.
Example 5: Finding Intercepts
Find the x- and y-intercepts.
–3x + 5y = 30
–3x + 5y = 30
–3x + 5(0) = 30
–3x – 0 = 30
–3x = 30
x = –10
The x-intercept is –10.
–3x + 5y = 30
–3(0) + 5y = 30
0 + 5y = 30
5y = 30
y=6
The y-intercept is 6.
Example 6: Finding Intercepts
Find the x- and y-intercepts.
4x + 2y = 16
4x + 2y = 16
4x + 2(0) = 16
4x + 0 = 16
4x = 16
x=4
The x-intercept is –10.
4x + 2y = 16
4(0) + 2y = 16
0 + 2y = 16
2y = 16
y=8
The y-intercept is 8.
Remember, to graph a linear function, you need
to plot only two ordered pairs. It is often
simplest to find the ordered pairs that contain
the intercepts.
Helpful Hint
You can use a third point to check your line. Either
choose a point from your graph and check it in the
equation, or use the equation to generate a point
and check that it is on your graph.