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Y-Intercept: Definition & Overview

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.

Definition

A y-intercept is the place where a line or curve crosses, or touches, the y-axis - the vertical, often darkened line in the center of a graph. It is also the point at which x = 0.

Y-intercepts and Graphs of Lines

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:

Graph of x + y = 5
Graph of a line

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.

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