Finding the x- and y-Intercepts of a Line
Objective Learn how to find the x- and
y-intercepts of a line and to use these points to graph the
equation of a line.
The x- and y-intercepts of a line are the points where the
line intersects the x- and y-axes, respectively. The diagram
shown will help convey this idea.
For the line graphed, the x-intercept is 4, and y-intercept is
3.
How can you find the x- and y-intercepts of a line given by an
equation?
If the equation is written in standard form or in point-slope
form, you can find the x- and y-intercepts by solving the
equation.
Consider the following examples.
Example 1
Find the x- and y- intercepts of y = -2x - 8.
Solution
| To find the x -intercept, let
y = 0. |
To find the y -intercept, let x = 0. |
| y |
= -2x - 8 |
y = -2x - 8 |
| 0 |
= -2x - 8 |
y = -2(0) - 8 |
| 0 + 8 |
= -2x - 8 + 8 |
y = 0 - 8 |
| 8 |
= -2x |
y = -8 |
 |
 |
The y -intercept is -8. |
| -4 |
= x |
The ordered pair is (0, -8). |
| The x -intercept is -4. |
|
| The ordered pair is ( -4, 0) |
Example 2
Find the x- and y- intercepts of 2x + 3y = 12.
Solution
| To find the x -intercept, let
y = 0. |
To find the y -intercept, let
x = 0. |
| 2x + 3y |
= 12 |
2x + 3y |
= 12 |
| 2x + 3(0) |
= 12 |
2(0) + 3y |
= 12 |
| 2x + 0 |
= 12 |
0 + 3y |
= 12 |
| 2x |
= 12 |
3y |
= 12 |
 |
 |
 |
 |
| x |
= 6 |
y |
= 4 |
| The x -intercept is 6. |
The y -intercept is 4. |
| The ordered pair is ( 6, 0) |
The ordered pair is (0, 4). |
