Y-intercept

If the curve in question is given as ${\displaystyle y=f(x),}$  the ${\displaystyle y}$ -coordinate of the ${\displaystyle y}$ -intercept is found by calculating ${\displaystyle f(0)}$ . Functions which are undefined at ${\displaystyle x=0}$  have no ${\displaystyle y}$ -intercept.

If the function is linear and is expressed in slope-intercept form as ${\displaystyle f(x)=a+bx}$ , the constant term ${\displaystyle a}$  is the ${\displaystyle y}$ -coordinate of the ${\displaystyle y}$ -intercept.^[2]

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

Analogously, an ${\displaystyle x}$ -intercept is a point where the graph of a function or relation intersects with the ${\displaystyle x}$ -axis. As such, these points satisfy ${\displaystyle y=0}$ . The zeros, or roots, of such a function or relation are the ${\displaystyle x}$ -coordinates of these ${\displaystyle x}$ -intercepts.^[3]

Functions of the form ${\displaystyle y=f(x)}$  have at most one ${\displaystyle y}$ -intercept, but may contain multiple ${\displaystyle x}$ -intercepts. The ${\displaystyle x}$ -intercepts of functions, if any exist, are often more difficult to locate than the ${\displaystyle y}$ -intercept, as finding the ${\displaystyle y}$ -intercept involves simply evaluating the function at ${\displaystyle x=0}$ .

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 ${\displaystyle I}$ -intercept of the current–voltage characteristic of, say, a diode. (In electrical engineering, ${\displaystyle I}$  is the symbol used for electric current.)

• Regression intercept