X-intercept

Definition

The x-intercept of a graph is the point where the graph intersects the x-axis. It occurs when the y-coordinate is zero.

5 Must Know Facts For Your Next Test

1. To find the x-intercept algebraically, set the y-variable to zero and solve for x.
2. In linear equations of the form $y = mx + b$, the x-intercept can be found by solving $0 = mx + b$ or $x = -\frac{b}{m}$.
3. A function can have multiple x-intercepts or none at all, especially in higher-degree polynomials and other types of functions.
4. Graphically, if a line crosses through (a,0) on the coordinate plane, then 'a' is an x-intercept.
5. X-intercepts are particularly useful in understanding the roots or solutions of equations.

Review Questions

• How do you determine the x-intercept of a linear equation?
• What happens to y at any point where there is an x-intercept?
• Can a quadratic function have more than one x-intercept? Explain.

Related terms

Y-Intercept: The y-intercept is where a graph intersects the y-axis, occurring when the x-coordinate is zero.

Slope: Slope measures the steepness and direction of a line, calculated as rise over run ($m = \frac{\Delta y}{\Delta x}$).

Root: A root of an equation is any value that makes the equation true when substituted for its variable; often corresponds to an intercept on a graph.