Finding Intercepts
An intercept is where a line crosses an axis.
First, let’s look at xintercepts. An x-intercept is where a graph crosses the x-axis. Its coordinates are of the form (x, 0).
Consider the linear equation 3x – 2y = 12. I could put this in slope-intercept form and graph it to find the xintercept…but that takes a lot of time. A faster way of finding the x-intercept is to plug in 0 for y! 3x – 2(0) = 12 3x = 12 x=4 So, the x-intercept of the linear function would be (4, 0).
Next, let’s look at yintercepts. A y-intercept is where a graph crosses the y-axis. Its coordinates are of the form (0, y).
Consider the linear equation 3x – 2y = 12. I could put this in slope-intercept form to find the y-intercept…but that takes a lot of time. A faster way of finding the y-intercept is to plug in 0 for x! 3(0) – 2y = 12 -2y = 12 y = -6 So, the 6-intercept of the linear function would be (0, -6).
You Try! Find the x-intercept and the yintercept of each linear function below. Then, turn the page to check your answers. 1. -2x + 5y = 10 2. 3x + 2y = 18
1. -2x + 5y = 10 x-intercept:
-2x + 5(0) = 10 -2x = 10 x = -5, so (-5, 0)
y-intercept:
-2(0) + 5y = 10 5y = 10 y = 2, so (0, 2)
2. 3x + 2y = 18 x-intercept:
3x + 2(0) = 18 3x = 18 x = 6, so (6, 0)
y-intercept:
3(0) + 2y = 18 2y = 18 y = 9, so (0, 9)