X and y intercepts

Math

Definition

The x-intercept is the point where a graph crosses the x-axis (y = 0), and the y-intercept is the point where a graph crosses the y-axis (x = 0). These intercepts are key features for graphing linear and nonlinear functions.

How It Works

  1. To find the x-intercept, set y = 0 and solve for x.
  2. To find the y-intercept, set x = 0 and solve for y.
  3. Plot both intercept points on the coordinate plane.
  4. Connect them (for a line) or use them as reference points for curves.

Examples

  • For y = 2x − 6: x-intercept is (3, 0) and y-intercept is (0, −6)
  • For y = x² − 9: x-intercepts are (3, 0) and (−3, 0), y-intercept is (0, −9)
  • The y-intercept of y = mx + b is always the point (0, b)
Key Fact

x-intercept: set y = 0; y-intercept: set x = 0

Related Terms

Slope-intercept form Standard form Zeros and end behavior Graphing systems

Study This Concept

Practice x and y intercepts with free review games in these units:

Algebra 1 Unit 3: Graphing Linear Functions