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In coordinate geometry, the y-intercept is the y-value of the point where the graph of a function or relation intercepts the y-axis of the coordinate system.
In other words, the y-intercept of a function is the y-value of the point at which it intersects the line x=0 (the y-axis). Thus, if the function is specified in form y = f(x), the y-intercept is easy to find by calculating f(0). For example, in linear equations that are in the "slope-intercept" form of y = mx + b, the value of b is the y-intercept. In general, in polynomial expressions of form y = P(x), where P is a polynomial, the constant term is the y-intercept of the polynomial. This is because all the other terms contain x and thus evaluate to zero when finding P(0).
If the function is undefined at x=0, for example y=cot(x), it has no y-intercept.
If the relationship is in the form f(x,y) = 0, or in the form of parametric equations, the corresponding equation (equations) must be solved. As a result, some 2-dimensional mathematical relationships such as circles, ellipses, and hyperbolas can have more than one y-intercept. A function of form y = f(x), however, has at most one y-intercept.
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 I/V-characteristic of, say, a diode. An x-intercept, or root, is the x-value of the point where a function intersects the x-axis, or the line y=0. Unlike y-intercepts, functions of the form y = f(x) can, and often do, contain multiple x-intercepts.
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- This page was last modified on 10 November 2008, at 02:39.
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