yintercept

The y-intercept is a term in Cartesian coordinate geometry referring to the point where a graph crosses the y-axis (the vertical axis, x = 0). For a function y = f(x), the y-intercept, when it exists, is the value f(0), represented by the point (0, f(0)).

In common forms for a line, the y-intercept has specific meaning. In slope-intercept form y = mx + b, the y-intercept is b, giving the point (0, b). More generally, for a line written as Ax + By = C with B ≠ 0, the y-intercept is (0, C/B). For the intercept form x/a + y/b = 1, the y-intercept is (0, b).

If a graph does not meet the y-axis, it has no y-intercept. A vertical line x = c with c ≠ 0 does not intersect the y-axis. The special case x = 0 describes the y-axis itself, which does not have a single y-intercept but rather every point along the axis lies on the axis.

Examples help illustrate the concept. The line y = 2x + 5 crosses the y-axis at (0, 5). The horizontal line y = -3 crosses at (0, -3). The vertical line x = 4 has no y-intercept.

The y-intercept concept extends to other curve representations as well: any intersection with the y-axis where x = 0 yields an intercept value y. It is commonly used in graph sketching and in understanding a function’s or curve’s behavior near the origin.