Everyone, throughout some of your graphing problems, you may be asked to identify these things called intercepts, and that's what I want to show you how to do in this video. Basically, what we're going to see here is that intercepts are really just special places or special points where the graph crosses either one of the x or y axis. So I'm going to show you how to identify those types of points and also some special things about them, and we'll do an example. Let's get started. Alright? So in this equation, I've got or in this diagram here, I've got 2 lines. I'm going to call this one a and this one b. Both of these graphs actually cross the x and y axis. If you look at line a, line a crosses the x-axis over here. Line b crosses the x-axis over here. These things are called the x-intercepts because that's where they cross the x-axis. So the x-intercept is where the graph crosses the x-axis. Now, similarly, these graphs also cross the y-axis over here and over here. So these points over here are called the y-intercepts. That is basically the y value where the graph crosses the y-axis. Alright? So pretty straightforward here. If you take a look at line a, line a crosses over here. So this is an x-intercept, where x is equal to negative 2. And over here, this is where x is equal to negative 4. So it's basically just the x value where that graph crosses the x-axis. Alright? And over here, what we've got is we got y = 4, and over here, we've got y = - 3. Alright? So that's what the y intercepts and x-intercepts are. Now what's sort of confusing about this is what happens to the other value. So, for example, in the x-intercepts, what you're going to see here is that the y value at any point along this line is always equal to 0 because you're basically right on the line, you have no height above it. So the x-intercept is where it crosses the x-axis, but it's also where the y value is equal to 0. Now, similarly, what happens for the y-intercept is that the x value is going to be 0. So notice how here, anytime you're on the y-axis, you're not to the right or to the left of the origin. So the y-intercept is where it crosses the y-axis, but the x value is always 0. That's kind of like the opposite. Alright? That's really all there is to know about x and y intercepts. So let's go ahead and do a quick example. So here, we're going to take this graph, and we're going to write the x and y intercepts of the graph that's shown below here. So remember, the x intercepts were crosses the x-axis. If you look at this line or this sort of curve shaped over here, this curve crosses the x-axis twice, once over here and what's over here. So what happens here is that the x-intercepts are just the values. It's just the number of the x coordinate. So in other words, our x-intercepts are negative 3 and positive 5. You don't have to write the ordered pair. You just have to write the numbers. Then what happens for the y-intercept? Well, this graph also crosses the y-axis over here. That's going to be a y-intercept. So your y-intercept over here is going to be y = - 4. So that's really all there is to it. Right? So let's take a look at another example here. We're now the question is written a little bit differently because instead of having to write the x-intercepts and y-intercepts, we're just asked to find the intercepts of the graph below. Okay? So let's take a look at that. So in this graph here, we've got this sort of like circle-looking thing, and notice how this graph actually crosses the x-axis right over here. So basically, what happens here is when they're asking for the intercepts, they're actually not asking for the x value. They're asking for the ordered pair. So that's sort of the real confusing thing with these sorts of problems. But, basically, if they ever ask for an x or a y intercept whenever they actually reference the letter by name, then all you actually have to do is just write the x or y value. But if they just ask you to find the intercepts as they are asking you in the second example, then you're going to write the ordered pair. So, really, all we have to do for the second example is just write the ordered pairs for these two numbers. And in this case, it's just going to be 2 comma 0, and then also so I'm going to write and, and then it's going to be 4 comma 0. So these are the intercepts of the graph, but these are the x and y intercepts of this graph. Alright. So that's really all there is to intercepts. Thanks for watching.
Table of contents
- 0. Fundamental Concepts of Algebra3h 29m
- 1. Equations and Inequalities3h 27m
- 2. Graphs1h 43m
- 3. Functions & Graphs2h 17m
- 4. Polynomial Functions1h 54m
- 5. Rational Functions1h 23m
- 6. Exponential and Logarithmic Functions2h 28m
- 7. Measuring Angles39m
- 8. Trigonometric Functions on Right Triangles2h 5m
- 9. Unit Circle1h 19m
- 10. Graphing Trigonometric Functions1h 19m
- 11. Inverse Trigonometric Functions and Basic Trig Equations1h 41m
- 12. Trigonometric Identities 2h 34m
- 13. Non-Right Triangles1h 38m
- 14. Vectors2h 25m
- 15. Polar Equations2h 5m
- 16. Parametric Equations1h 6m
- 17. Graphing Complex Numbers1h 7m
- 18. Systems of Equations and Matrices1h 6m
- 19. Conic Sections2h 36m
- 20. Sequences, Series & Induction1h 15m
- 21. Combinatorics and Probability1h 45m
- 22. Limits & Continuity1h 49m
- 23. Intro to Derivatives & Area Under the Curve2h 9m
2. Graphs
Two-Variable Equations
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