What is a Secant Line?

A secant line is a straight line that intersects a curve at two points. It is essentially a line that connects two points on a curve. The term "secant" comes from the Latin word "secare," which means "to cut." Therefore, a secant line can be thought of as a line that cuts through a curve at two distinct points.

Use of Secant Lines

Secant lines are commonly used in mathematics to approximate the slope of a curve at a specific point. By drawing a secant line that passes through two points close to each other on the curve, we can estimate the slope of the curve at that point. As the two points get closer together, the secant line more closely approximates the tangent line to the curve at that point.

Relation to Tangent Lines

While a secant line intersects a curve at two points, a tangent line touches a curve at only one point. The slope of a secant line can help us estimate the slope of a tangent line at a certain point on the curve. In calculus, the concept of secant lines is often used to understand the behavior of functions and to find derivatives.