In
analytic geometry
In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry.
Analytic geometry is used in physics and enginee ...
, 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
graph of a function
In mathematics, the graph of a function f is the set of ordered pairs (x, y), where f(x) = y. In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subs ...
or
relation intersects the ''y''-axis of the
coordinate system
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is sig ...
. As such, these points satisfy ''x'' = 0.
Using equations
If the curve in question is given as
the ''y''-coordinate of the ''y''-intercept is found by calculating
Functions which are undefined at ''x'' = 0 have no ''y''-intercept.
If the function is
linear
Linearity is the property of a mathematical relationship ('' function'') that can be graphically represented as a straight line. Linearity is closely related to '' proportionality''. Examples in physics include rectilinear motion, the linear ...
and is expressed in
slope-intercept form as
, the constant term
is the ''y''-coordinate of the ''y''-intercept.
Multiple y-intercepts
Some 2-dimensional mathematical relationships such as
circle
A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is cons ...
s,
ellipse
In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special type of ellipse in ...
s, and
hyperbola
In mathematics, a hyperbola (; pl. hyperbolas or hyperbolae ; adj. hyperbolic ) is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, ca ...
s can have more than one ''y''-intercept. Because
functions 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 the
graph of a function
In mathematics, the graph of a function f is the set of ordered pairs (x, y), where f(x) = y. In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subs ...
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 the
current–voltage characteristic of, say, a
diode
A diode is a two-terminal electronic component that conducts current primarily in one direction (asymmetric conductance); it has low (ideally zero) resistance in one direction, and high (ideally infinite) resistance in the other.
A diod ...
. (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 l ...
, ''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 movi ...
.)
See also
*
Regression intercept
References
{{DEFAULTSORT:Y-Intercept
Elementary mathematics
Functions and mappings