Using Intercepts for Graphing Linear Equations
The x-intercept of a line is the point where the line crosses the x-axis.
The x-intercept has a y-coordinate of 0. Similarly, the y-intercept of a
line is the point where the line crosses the y-axis. The y-intercept has an x-coordinate
of 0. If a line has distinct x- and y-intercepts, then these intercepts can be
used as two points that determine the location of the line. (Horizontal lines,
vertical lines, and lines through the origin do not have two distinct intercepts.)
Example 1
Using intercepts to graph
Use the intercepts to graph the line 3x - 4y = 6.
Solution
Let x = 0 in 3x - 4y = 6 to find the y-intercept:
| 3(0) - 4y |
= 6 |
| -4y |
= 6 |
| y |
 |
Let y = 0 in 3x - 4y = 6 to find the x-intercept:
| 3x - 4(0) |
= 6 |
| 3x |
= 6 |
| x |
= 2 |
The y-intercept is ,
and the x-intercept is (2, 0). The line through the intercepts is shown in the
figure below. To check, find another point that satisfies the equation. The
point (-2, -3) satisfies the equation and is on the line in the figure below.
Caution
Even though two points determine the location of a line, finding at least
three points will help you to avoid errors.
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