IntroFoundations

Secant vs Tangent Line

Overview

Two kinds of lines on a curve. A secant cuts through at two points — measuring average change. A tangent touches at one point — measuring instantaneous change.

Key Concepts

1

Secant line: connects two distinct points on the curve → average rate of change

2

Tangent line: touches the curve at exactly one point → instantaneous rate

3

As the two secant points get closer, the secant → the tangent line

4

The slope of the tangent at x = a is the derivative f′(a)

See it in action

Use the interactive visualizer to explore this concept with real graphs.

Open Derivative Explorer