A secant line, also simply called a secant, is a line passing through two points of a curve. As the two points are brought together (or, more precisely, as one is brought towards the other), the secant line tends to a tangent line.
The secant line connects two points 
and 
in the Cartesian plane
on a curve described by a function 
. It gives the average
rate of change of 
from 
to 
 |
(1)
|
which is the slope of the line connecting the points 
and 
. The limiting value
 |
(2)
|
as the point 
approaches 
gives the instantaneous slope of the tangent
line to 
at each point 
,
which is a quantity known as the derivative of 
, denoted 
or 
.
The use of secant lines to iteratively find the root of a function is known as the secant method.
In abstract mathematics, the points connected by a secant line can be either real or complex conjugate imaginary.
In geometry, a secant line commonly refers to a line that intersects a circle at exactly two points (Rhoad et al. 1984, p. 429). There are a number of interesting theorems related to secant lines.
In the left figure above,
 |
(3)
|
while in the right figure,
 |
(4)
|
where 
denotes the angular measure of the arc 
(Jurgensen 1963, pp. 336-337).
