Y-intercept

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 $$f(x) = a + bx$$, 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.)