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.

^{[1]}As such, these points satisfy

*x*= 0.

## Contents

## Using equations

If the curve in question is given as the *y*-coordinate of the *y*-intercept is found by calculating 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 is the *y*-coordinate of the *y*-intercept.^{[2]}

## 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.^{[3]}

Unlike *y*-intercepts, functions of the form *y* = *f*(*x*) 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.)

## See also

## References

**^**Weisstein, Eric W. "y-Intercept". MathWorld--A Wolfram Web Resource. Retrieved 2010-09-22.**^**Stapel, Elizabeth. "x- and y-Intercepts." Purplemath. Available from http://www.purplemath.com/modules/intrcept.htm.**^**Weisstein, Eric W. "Root". MathWorld--A Wolfram Web Resource. Retrieved 2010-09-22.