x-Intercept of a Line

A line crosses the x-axis where y = 0, so setting 0 = mx + b and solving gives x = −b/m. Worked example: y = 2x − 6 meets the axis at x = 6/2 = 3, the point (3, 0). It is the same thing as the root of the linear function, and the linear cousin of the quadratic formula: one root instead of two, because a straight line can only cross once.

Intercepts are how you sketch a line in seconds: plot (0, b) and (−b/m, 0), then join them. They also carry the meaning in applied problems. A tank draining as V = 500 − 25t empties when 25t = 500, at t = 20 minutes; a business whose profit runs P = 40n − 1200 breaks even at n = 30 units. The traps are the minus sign (the intercept of y = 2x − 6 is +3, because −(−6)/2 = 3) and the horizontal case, where m = 0 means the line never crosses at all unless it already lies on the axis. Note that b and the x-intercept are both lengths here while the slope is a pure ratio, so you can enter the intercept in one unit and read the crossing point in another.