The x-intercept of a line is the point where it crosses the x-axis (found by setting y to zero); the y-intercept is where it crosses the y-axis (found by setting x to zero). Learn to find both from an equation, and how two intercepts are enough to graph a whole line.
What x- and y-intercepts are
The x-intercept is the point where a line crosses the x-axis; the y-intercept is where it crosses the y-axis. At the x-intercept, y = 0. At the y-intercept, x = 0.
Finding the x-intercept
Set y = 0 in the equation and solve for x. For 2x + 3y = 6, substituting y = 0 gives 2x = 6, so x = 3 — the x-intercept is (3, 0).
Finding the y-intercept
Set x = 0 and solve for y. For the same equation, substituting x = 0 gives 3y = 6, so y = 2 — the y-intercept is (0, 2).
The x-intercept and y-intercept of 2x + 3y = 6, found by setting the other variable to zero.
Why intercepts matter
Two intercepts are enough to draw an entire straight line: plot both points and connect them. This is why intercepts are one of the fastest ways to graph a linear function, and they show up again when you study horizontal lines (which have no x-intercept unless they lie on the x-axis) and vertical lines (which have no y-intercept unless they lie on the y-axis).