Y-intercept

Y-intercept

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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