1. y-intercept: y-coordinate of the point where the graph intersects the y-axis. The x-coordinate of this point is always 0, i.e., (0, #).
x-intercept: x-coordinate of the point where the graph intersects the x-axis. The y-coordinate of this point is always 0, i.e., (#, 0).

2. 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.

3. 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.

4. 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.

5. 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 – 2y = 10
5(0) – 2y = 10
5x – 0 = 10
5x = 10
0 – 2y = 10
– 2y = 10
x = 2
The x-intercept is 2.
y = –5
The y-intercept is –5.

6. Example 5: Finding Intercepts
Find the x- and y-intercepts.
–3x + 5y = 30
–3x + 5y = 30
–3x + 5(0) = 30
–3x + 5y = 30
–3(0) + 5y = 30
–3x – 0 = 30
–3x = 30
0 + 5y = 30
5y = 30
y = 6
The y-intercept is 6.
x = –10
The x-intercept is –10.

7. Example 6: Finding Intercepts
Find the x- and y-intercepts.
4x + 2y = 16
4x + 2y = 16
4x + 2(0) = 16
4x + 2y = 16
4(0) + 2y = 16
4x + 0 = 16
4x = 16
0 + 2y = 16
2y = 16
y = 8
The y-intercept is 8.
x = 4
The x-intercept is –10.

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.