Secant line

A secant line intersects a curve at two points. Its slope gives the average rate of change of the curve’s output between those points.

Difference quotient: A ratio of the change in a function’s values to the change in its input. It computes the secant line’s slope from the two points.
Coordinate plane: A plane with perpendicular axes used to locate points by ordered pairs of numbers. It provides the coordinates needed to identify points on a graph.
Finite difference: An approximation to a derivative formed from function values at distinct inputs. A finite-difference quotient is the numerical counterpart of a secant slope.
Tangent-secant theorem: A circle theorem relating a tangent segment and a secant segment from the same external point. It uses secant lines in circle geometry rather than as average-change approximations.
Average rate of change: The change in a quantity divided by the change in an independent variable over an interval. The secant slope expresses this rate for a function across two inputs.
Function: A rule that assigns each input in its domain exactly one output. A function’s graph supplies the curve whose two points define a secant.
Numerical differentiation: The estimation of derivatives from discrete or approximate function values. It uses secant slopes when an exact derivative is unavailable or inconvenient.
Chord (geometry): A line segment whose endpoints lie on a curve, especially on a circle. A circle’s secant intersects at two points, and the portion between them is a chord.
Limit of a function: The value a function approaches as its input approaches a specified point. It formalizes what happens to secant slopes as their points draw together.
Graph of a function: The set of points pairing each input with its function output in a coordinate plane. A secant is drawn through two points selected from this graph.

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