In analytic geometry, using the common convention that the horizontal axis represents a variable x and the vertical axis represents a variable y, a y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system. As such, these points satisfy x = 0.

Using equations

If the curve in question is given as y = f(x), the y-coordinate of the y-intercept is found by calculating f(0). Functions which are undefined at x = 0 have no y-intercept. If the function is linear and is expressed in slope-intercept form as, the constant term a is the y-coordinate of the y-intercept.

Multiple y -intercepts

Some 2-dimensional mathematical relationships such as circles, ellipses, and hyperbolas can have more than one y-intercept. Because functions associate x-values to no more than one y-value as part of their definition, they can have at most one y-intercept.

x -intercepts

Analogously, an x-intercept is a point where the graph of a function or relation intersects with the x-axis. As such, these points satisfy y = 0. The zeros, or roots, of such a function or relation are the x-coordinates of these x-intercepts. Functions of the form y = f(x) have at most one y-intercept, but may contain multiple x-intercepts. The x-intercepts of functions, if any exist, are often more difficult to locate than the y-intercept, as finding the y-intercept involves simply evaluating the function at x = 0.

In higher dimensions

The notion may be extended for 3-dimensional space and higher dimensions, as well as for other coordinate axes, possibly with other names. For example, one may speak of the I-intercept of the current–voltage characteristic of, say, a diode. (In electrical engineering, I is the symbol used for electric current.)