Finding x- and y-intercepts
The point where a graph crosses an axis called an intercept.
Definition
x-intercept and y-intercept
| The x-intercept is the point
where the line crosses the x-axis.
The x-intercept has the form
(a, 0), where a is a constant.
The y-intercept is the point
where the line crosses the y-axis.
The y-intercept has the form
(0, b), where b is a constant. |
 |
Note:
The x-intercept lies on the x-axis, so y = 0.
The y-intercept lies on the y-axis, so x = 0.
Example 1
Given the equation 4x - 8y = 16:
a. Find the x-intercept.
b. Find the y-intercept.
c. Use the intercepts to graph the line.
Solution
| a. The x-intercept has the form (a, 0).
To find the x-intercept, substitute 0 for y.
Then, solve for x.
The x-intercept is (4, 0). |
4x - 8y = 16 4x - 8(0)= 16
4x - 0 = 16
4x = 16
x = 4 |
| b. The y-intercept has the form (0, b).
To find the y-intercept, substitute 0 for x.
Then, solve for y.
The y-intercept is (0, -2) |
4x - 8y = 16 4(0) - 8y = 16
0 - 8y = 16
-8y = 16
y = -2 |
| c. To graph the line 4x - 8y = 16, first plot
the x- and y-intercepts.
Then, draw a line through the intercepts. x-intercept
As a check, it is a good idea to find a third y-intercept
point on the line. |
 |
| For example, let x = -2 in 4x - 8y = 16. Then, solve for y.
The result is y = -3. So, the point (-2, -3) should also lie on the line. |
|