Y-intercept explained

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

See main article: Zero of a function. 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.)

See also

• Regression intercept

References

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