Intercepts of a Line
Pre-algebra students in OpenStax Prealgebra 2E learn to identify x-intercepts and y-intercepts as the points where a line crosses the coordinate axes. The x-intercept is the point (a, 0) found by setting y = 0 and solving. The y-intercept is the point (0, b) found by setting x = 0 and solving. A line crossing the x-axis at (8, 0) has x-intercept 8; passing through (0, -5) has y-intercept -5. Intercepts are used to graph lines, write equations, and analyze linear relationships.
Key Concepts
Property Each of the points at which a line crosses the $x$ axis and the $y$ axis is called an intercept of the line.
The $x$ intercept is the point, $(a, 0)$, where the graph crosses the $x$ axis. The $x$ intercept occurs when $y$ is zero.
The $y$ intercept is the point, $(0, b)$, where the graph crosses the $y$ axis. The $y$ intercept occurs when $x$ is zero.
Common Questions
What is an x-intercept?
The x-intercept is the point where a line crosses the x-axis. It has coordinates (a, 0) because y is always 0 on the x-axis.
What is a y-intercept?
The y-intercept is the point where a line crosses the y-axis. It has coordinates (0, b) because x is always 0 on the y-axis.
How do you find the x-intercept of a line algebraically?
Set y = 0 in the equation and solve for x. The solution is the x-intercept.
How do you find the y-intercept algebraically?
Set x = 0 in the equation and solve for y. The solution is the y-intercept.
Can a line have more than one x-intercept or y-intercept?
A non-vertical line has exactly one y-intercept and at most one x-intercept. A horizontal line at y = 0 (the x-axis) has infinitely many x-intercepts.