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X and Y Intercepts of a Line
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Introduction

In this lesson, you will review how to find the x- and y-intercepts of a line.


This video illustrates the lesson material below. Watching the video is optional.


X- and Y-Intercepts

Intercepts are an important part of graphs. They indicate a lot about data. For example, y-intercepts often give a starting amount. Here are some vocabulary words to help you with this lesson:

  • x-intercept: where the graph crosses the x-axis, and where \(y = 0\)
  • y-intercept: where the graph crosses the y-axis, and where \(x = 0\)

The x-intercept is anywhere that the line crosses the x-axis. The x-axis is also known as the horizontal axis. The y-intercept is anywhere that the line crosses the y-axis.

This figure shows the x-intercept crosses point 1.5 in the x-axis and y is zero. The y-intercept crosses point 3 in the y-axis and x is zero.

Figure 1

At the y-intercept point, \(x=0\). Similarly, at the point at which the line crosses the x-axis, \(y=0\). At the point where the line crosses the x-axis, y will always be 0. The value of x will change depending on the line, but any time the line crosses the x-axis, \(y=0\).

Any time the line crosses the y-axis, x has to be 0. The value of y may be different, but the y will be where it crosses.

This figure shows that at y-intercept point, x = 0. The same goes for x-intercept point.

Figure 2

When you know this information, you still need to estimate the value of x for the x-intercept and the value of y for the y-intercept.

Example 1
Estimate the y-intercept of the line in Figure 2.

If you look at the x-intercept, you can estimate it at 1.5. The estimated x-intercept is written as: \((1.5, 0)\). The y-intercept is approximately at 3. The estimated y-intercept is written as \((0, 3)\).


Things to Remember

  • At the x-intercept point, \(y=0\).
  • At the y-intercept point, \(x=0\).

Practice Problems

Use the following graph to answer questions 1 through 6.This is an image of a graph with five different lines. Line A starts in the top left and ends in the bottom right. Line B starts in the bottom left and ends in the top right. Line C starts in the top left and ends in the bottom right. Line D starts around the lower middle area of the left side and ends in the upper middle area of the right side. Line E starts around the x axis on the left and ends 4 units down from the x axis on the right.
  1. What is the y-intercept of line A? (
    Solution
    x
    Solution:
    Y-intercept: \(-4\)
    )
  2. What is the x-intercept of line B? (
    Solution
    x
    Solution:
    X-intercept: \(0\)
    )
  3. What is the y-intercept of line B? (
    Solution
    x
    Solution:
    Y-intercept: \(0\)
    )
  4. What are the x-intercept and y-intercept of line C? (
    Solution
    x
    Solution:
    X-intercept: \(1.5\)
    Y-intercept: \(3\)

    Details:
    To find the x-intercept, look for the point where the line crosses the x-axis. The line crosses the x-axis where the x-value is approximately \(1.5\). The y-value is always \(0\) for every point on the x-axis so the x-intercept is \((1.5, 0)\).

    To find the y-intercept, look for the point where the line crosses the y-axis. The line crosses the y-axis where the y-value is \(3\). The x-value is always \(0\) for every point on the y-axis so the y-intercept is \((0, 3)\).
    This is a picture of a coordinate plane with several lines graphed. The line marked C has an arrow pointing at the y-intercept, which is the point (0, 3). There is an arrow pointing at the x-intercept, which is the point (1.5, 0).
    )
  5. What are the x-intercept and y-intercept of line D? (
    Solution
    x
    Solution:
    X-intercept: \(-3\)
    Y-intercept: \(1\)

    Details:
    To find the x-intercept, look for the point where the line crosses the x-axis. The line crosses the x-axis where the x-value is approximately \(-3\). The y-value is always 0 for every point on the x-axis so the x-intercept is \((-3,0)\).

    To find the y-intercept, look for the point where the line crosses the y-axis. The line crosses the y-axis where the y-value is \(1\). The x-value is always 0 for every point on the y-axis so the y-intercept is \((0, 1)\).
    A coordinate plane with several lines graphed. The line marked C has an arrow pointing at the y intercept, which is the point (0, 1). There is an arrow pointing at the x intercept, which is the point (negative 3,0).
    )
  6. What are the x-intercept and y-intercept of line E? (
    Solution
    x
    Solution:
    X-intercept: \(-5\)
    Y-intercept: \(-2\)
    )

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