Study Guide

Basic Algebra - Intercepts

Intercepts

The x- and y-intercepts of a line are the points where the line intercepts, or crosses, either the x-axis or the y-axis.

  • x-intercept: the point where the line crosses the x-axis. Notice that the y-value is 0.
  • y-intercept: the point where the line crosses the y-axis. Notice that the x-value is 0.

An intercept can be written in (x, y) form or in words, like "the x-intercept is 2." It can't be written as x = 2, because this is an equation of a vertical line going through the point (2, 0).

Let's find the y-intercept of the equation y = 2x + 1. To find the y-intercept, we substitute 0 in for x and then solve for y.

y = 2(0) + 1
y = 1

So the y–intercept is where x = 0 and y ¬= 1, or the point (0, 1).

To find the x-intercept, we replace y with 0 and then solve for x. First off, subtract 1 from both sides.

0 = 2x + 1
0 – 1 = 2x + 1 – 1
-1 = 2x

Now divide both sides by 2.

So the y-intercept is where , or the point .