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GMAT Prep: Tutoring Solution23 chapters | 224 lessons

Instructor:
*Kimberlee Davison*

Kim has a Ph.D. in Education and has taught math courses at four colleges, in addition to teaching math to K-12 students in a variety of settings.

In this lesson, you will learn about the y-intercept, a particular point (or several points) on a graph where the line or curve touches or crosses the y-axis.

A ** y-intercept** is the place where a line or curve crosses, or touches, the

Suppose you have two individuals, such as a married couple, and they share the household tasks between them. Let's call them Hope and Stealth. Hope and Stealth have decided to get a certain amount of household work completed each day. If Hope does more, Stealth does less. If Stealth does more, Hope does less.

To keep things simple, assume that there are 5 chores to be done. So, if Hope does 3, Stealth does 2. If Hope does 1, Stealth does 4. Or maybe Hope does 2.63 tasks and Stealth finishes up the other 2.37.

The point here is that there is a relationship between what Hope does and what Stealth does that can be defined precisely by an equation. If you know what one does, finding out what the other does just takes some calculation.

You might write it like this:

Stealth + Hope = 5

OR

x + y = 5

Stealth is the *x* and Hope is the *y*.

Or, you might even rearrange it into **slope-intercept** form (*y* on the left and everything else on the right) like this:

y = -x + 5

If we want to understand the relationship more clearly visually, we might use a graph:

Any point on the graph tells us how many chores Hope does if Stealth does some given amount.

Of course, it's possible that Hope may have to do all of the chores, because Stealth snuck off to watch the annual city Groundhog's Day parade. In this case, Hope does 5 chores and Stealth does 0.

If you look at the graph, you will see that the point where Stealth is 0 and Hope is 5 hits right at the central, vertical line - the *y*-axis. Since this point touches, or *intercepts*, the *y*-axis, it is called the *y*-intercept. The *y*-intercept is also the point at which the other variable, *x*, is zero.

It's possible for something you graph, such as a curve, to hit the *y*-axis more than one time. For example, in the graph below, the circle hits the *y*-axis twice. In this case there are two *y*-intercepts.

In the graph of the circle, there is a *y*-intercept at *y*= 3 and another *y*-intercept at *y* = -2.

Having more than one *y*-intercept is perfectly fine if it makes sense for the equation you graph. Some equations will have no *y*-intercepts, some will have one, and others will have several.

A *y*-intercept is the point at which a line or curve hits the *y*-axis, the place where *x* = 0. There can, in some cases, be several *y*-intercepts, or there can be none.

When you are finished, you should be able to:

- Explain what the y-intercept on a graph is
- Recall what slope-intercept form is
- Identify the y-intercept(s) on a graph

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15 in chapter 14 of the course:

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GMAT Prep: Tutoring Solution23 chapters | 224 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
- How to Find and Apply The Slope of a Line 9:27
- How to Find and Apply the Intercepts of a Line 4:22
- Graphing Undefined Slope, Zero Slope and More 4:23
- Equation of a Line Using Point-Slope Formula 9:27
- How to Use The Distance Formula 5:27
- How to Use The Midpoint Formula 3:33
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- Parabolas in Standard, Intercept, and Vertex Form 6:15
- How to Graph Cubics, Quartics, Quintics and Beyond 11:14
- Compound Inequality: Definition & Concept
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