In analytic geometry, using the common convention that the horizontal axis represents a variable and the vertical axis represents a variable , a -intercept or vertical intercept is a point where the graph of a function or relation intersects the -axis of the coordinate system.[1] As such, these points satisfy .

Graph with the -axis as the horizontal axis and the -axis as the vertical axis. The -intercept of is indicated by the red dot at .

Using equations

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If the curve in question is given as   the  -coordinate of the  -intercept is found by calculating  . Functions which are undefined at   have no  -intercept.

If the function is linear and is expressed in slope-intercept form as  , the constant term   is the  -coordinate of the  -intercept.[2]

Multiple -intercepts

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

-intercepts

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Analogously, an  -intercept is a point where the graph of a function or relation intersects with the  -axis. As such, these points satisfy  . The zeros, or roots, of such a function or relation are the  -coordinates of these  -intercepts.[3]

Functions of the form   have at most one  -intercept, but may contain multiple  -intercepts. The  -intercepts of functions, if any exist, are often more difficult to locate than the  -intercept, as finding the  -intercept involves simply evaluating the function at  .

In higher dimensions

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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  -intercept of the current–voltage characteristic of, say, a diode. (In electrical engineering,   is the symbol used for electric current.)

See also

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References

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