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.^[1] 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.^[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]

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.)

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.