y-intercept

The y-intercept is where a graph meets the y-axis — its “starting height” when x is 0. If a line described your bank balance over time, the y-intercept would be how much you began with.

Because it sits on the y-axis, the y-intercept always has the form (0, b). You find it by setting x = 0 and computing y. In the line y = mx + b, the constant b is exactly the y-intercept’s height, which is why that form is so convenient.

A function has at most one y-intercept (only one output is possible at x = 0), but it may have none — for instance, a vertical line x = 3 never touches the y-axis at all.