analytic geometry In 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 engineering, and als ...

, 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 a plane (geometry), plane and often form a P ...

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 and standardize the position of the points or other geometric elements on a manifold such as Euclidean space. The coordinates are ...

. 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 is

linear In mathematics, the term ''linear'' is used in two distinct senses for two different properties: * linearity of a '' function'' (or '' mapping''); * linearity of a '' polynomial''. An example of a linear function is the function defined by f(x) ...

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 as

circle 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. The distance between any point of the circle and the centre is cal ...

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. It generalizes a circle, which is the special ty ...

s, and

hyperbola In mathematics, a hyperbola is a type of smooth function, smooth plane curve, 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, called connected component ( ...

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

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. {{Cite web , last = Weisstein , first = Eric W. , title = Root , publisher = MathWorld--A Wolfram Web Resource , url = http://mathworld.wolfram.com/Root.html , access-date = 2010-09-22 Functions of the form

y = f(x)

have at most one

y

-intercept, but 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 A current–voltage characteristic or I–V curve (current–voltage curve) is a relationship, typically represented as a chart or graph, between the electric current through a circuit, device, or material, and the corresponding voltage, or p ...

of, say, a

diode A diode is a two-Terminal (electronics), terminal electronic component that conducts electric current primarily in One-way traffic, one direction (asymmetric electrical conductance, conductance). It has low (ideally zero) Electrical resistance ...

. (In

electrical engineering Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems that 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 flow of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is defined as the net rate of flow of electric charge through a surface. The moving particles are called charge c ...

References

Elementary mathematics Functions and mappings

Using equations

Multiple y-intercepts

x-intercepts

In higher dimensions

See also

References

Multiple $y$ -intercepts

$x$ -intercepts