What is a secant line?

A secant line is a straight line that intersects a curve at two distinct points. It is a useful concept in mathematics and is often used in calculus to approximate the slope of a curve at a specific point.

The slope of a secant line is given by the difference in the y-values divided by the difference in the x-values of the two points where the secant line intersects the curve. This slope provides an approximation of the instantaneous rate of change of the curve at that point.

Secant lines are also used to calculate the average rate of change of a function over an interval. By finding the slope of the secant line between two points on the curve, one can estimate the average rate of change of the function over that interval.

In geometry, secant lines are often used in relation to circles. A secant line intersects a circle at two points, creating a chord that lies entirely within the circle. The length of the chord and its distance from the center of the circle can be used to calculate various properties of the circle.