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ELM: CSU Math Study Guide16 chapters | 140 lessons

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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.

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.

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.

This may make more sense when looking at some lines. Let's start with this one: *y* = 3*x* + 6. What's the x-intercept? Remember, we want to know what *x* is. So make *y* = 0. That's 0 = 3*x* + 6. We get 3*x* = -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.

Ok, that was a tricky one. Let's try this one: 2*x* + 3*y* = 12. What's the x-intercept? Just make *y* = 0 and solve for *x*! We start with 2*x* + 3(0) = 12. Ok, 2*x* = 12. *x* = 6. So this line crosses the x-axis at *x* = 6, which is also (6, 0).

What about the y-intercept? Just make *x* = 0! 2(0) + 3*y* = 12. That's 3*y* = 12. Divide by 3 and you get *y* = 4. So it crosses the y-axis at (0, 4).

If we put those two points on a graph, then connect the dots, that's our line! What a nice line we've made. But wait. How can we be sure we made the right line? Let's test it! It looks like this line also goes through (3, 2). Will those values for *x* and *y* work in our equation? Remember, it's 2*x* + 3*y* = 12. So 2(3) + 3(2) = 12. That's 6 + 6 = 12. It works! If only finding my way when I'm driving was this easy!

In summary, the **x-intercept** is the spot where a line crosses the x-axis. To find it, just make *y* = 0, then solve for *x*. The **y-intercept** is the spot where a line crosses the y-axis. To find this one, just make *x* = 0, then solve for *y*.

After working this lesson and practice, you should be able to define x- and y-intercepts and, with confidence, find x- and y-intercepts mathematically.

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5 in chapter 15 of the course:

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ELM: CSU Math Study Guide16 chapters | 140 lessons

- Graph Functions by Plotting Points 8:04
- Identify Where a Function is Linear, Increasing or Decreasing, Positive or Negative 5:49
- Linear Equations: Intercepts, Standard Form and Graphing 6:38
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- How to Find and Apply the Intercepts of a Line 4:22
- Equation of a Line Using Point-Slope Formula 9:27
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- How to Use The Midpoint Formula 3:33
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