Image:Y-intercept.svg, 300px, Graph ''y''=''ƒ''(''x'') with the ''x''-axis as the horizontal axis and the ''y''-axis as the vertical axis. The ''y''-intercept of ''ƒ''(''x'') is indicated by the red dot at (''x''=0, ''y''=1).
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

{{DEFAULTSORT:Y-Intercept
Elementary mathematics

graph of a function
In mathematics
Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). ...

or relation intersects the ''y''-axis of the coordinate system
In geometry
Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' "earth", ''wikt:μέτρον, -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space t ...

. 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 islinear
Linearity is the property of a mathematical relationship (''function
Function or functionality may refer to:
Computing
* Function key
A function key is a key on a computer
A computer is a machine that can be programmed to carry out se ...

and is expressed in slope-intercept form as $f(x)=a+bx,$ the constant term $a$ is the ''y''-coordinate of the ''y''-intercept.
Multiple y-intercepts

Some 2-dimensional mathematical relationships such ascircle
A circle is a shape consisting of all point (geometry), points in a plane (mathematics), plane that are at a given distance from a given point, the Centre (geometry), centre; equivalently it is the curve traced out by a point that moves in a ...

s, ellipse
In mathematics, an ellipse is a plane curve surrounding two focus (geometry), focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. As such, it generalizes a circle, which is the sp ...

s, and hyperbola
300px, Hyperbola (red): features
In mathematics
Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (ma ...

s can have more than one ''y''-intercept. Because functions
Function or functionality may refer to:
Computing
* Function key
A function key is a key on a computer
A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations automatically. Modern comp ...

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

Analogously, an ''x''-intercept is a point where thegraph of a function
In mathematics
Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). ...

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.
Unlike ''y''-intercepts, functions of the form ''y'' = ''f''(''x'') 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 thecurrent–voltage characteristic
A current–voltage characteristic or I–V curve (current–voltage curve) is a relationship, typically represented as a chart
A chart is a graphical representation for data visualization, in which "the data
Data are units of inform ...

of, say, a diode
Various semiconductor diodes. Bottom: A bridge rectifier. In most diodes, a white or black painted band identifies the cathode into which electrons will flow when the diode is conducting. Electron flow is the reverse of conventional current flow ...

. (In electrical engineering
Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the la ...

, ''I'' is the symbol used for electric current
An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The moving part ...

.)
See also

*Regression intercept
In statistics
Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin wit ...

References