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How to Find and Apply the Intercepts of a Line

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  • 0:06 Intercepts
  • 0:31 X- and Y-Intercepts
  • 1:33 Practice Problems
  • 4:01 Lesson Summary
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Lesson Transcript
Instructor: Jeff Calareso

Jeff teaches high school English, math and other subjects. He has a master's degree in writing and literature.

How can you take an equation of a line and find out where it will cross the x- or y-axis? In this lesson, we'll define x-intercepts and y-intercepts and learn how to find them.

Intercepts

Sometimes, when I'm driving, I'm not sure how to get to where I'm going. I may be going down a road with a vague idea that it will connect with another road. Yet, I'm not 100% sure of that, and even if it does, I don't know where that will happen. What I want to know is where my road will intercept with another. That's the concept we're going to learn about here. But we're going to look at intercepts in terms of graphs, not me getting lost.

X- And Y-Intercepts

But just like roads in the real world, lines on graphs intercept with the graphs' axes. There are two kinds of intercepts: x-intercepts and y-intercepts. The x-intercept of a line is the place where the line crosses the x-axis. That means it's the place where y = 0. The y-intercept of a line is the place where a line crosses the y-axis. That means it's the place where x = 0.

In both cases, there's a simple way to figure out the intercepts. Just take the equation of the line and make one of the variables zero. Then solve for the other variable. Whatever that variable equals, that's where your line crosses the axis.

The hardest part of intercepts is remembering which variable to make zero. Again, with x-intercepts, y = 0, and with y-intercepts, x = 0. Just keep your focus on the goal. If we want to know the x-intercept, we'll want to know what x is. Think about that for a second. You need y to be 0 for the x-intercept, because the x-axis is where y always is zero.

Practice Problems

This may make more sense when looking at some lines. Let's start with this one: y = 3x + 6. What's the x-intercept? Remember, we want to know what x is. So make y = 0. That's 0 = 3x + 6. We get 3x = -6. Divide by 3 and you get x = -2. So this line crosses the x-axis at x = -2, which we write as (-2, 0).

What about the y-intercept? Here, we want to know what y is, so make x = 0. So y = 3x + 6 becomes y = 3(0), which disappears, + 6. That's just y = 6. So it's going to cross the y-axis at y = 6, or (0, 6). Let's put those dots on a graph. Then you can connect the dots and we have our line!

Let's try another line: y = 2. Wait, what? Is that a line? It is. But how can you find the x-intercept? If you make y = 0, you'd get 0 = 2, which is impossible. That's because the line of y = 2 looks like this. It's a horizontal line. It intercepts the y-axis at 2, but it never intercepts the x-axis. It's parallel to the x-axis.

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