How to find the equation of a secant line given two points?

We will use the two-point form to find the equation of a secant line.

Answer: The equation of a secant line given two points (a, b) and (c, d) is y - b = [(d - b)/(c - a)] (x - a)

Let's understand the equation of a secant line given two points.

Explanation:

Let two points joining a secant line be (a, b) and (c, d).

The equation of a secant line joining two points (a, b) and (c, d) is y - b = [(d - b)/(c - a)] (x - a)

Here, (d - b)/(c - a) is the slope of the secant line joining the points (a, b) and (c, d).

Consider an example to understand better.

Let's find the equation of a line joining two points (1, 3) and (-2, 5).

Slope = (5 - 3)/(-2 - 1) = -2/3

You can find the slope using Cuemath's Slope Calculator.

Equation of line: y - 3 = -2/3 (x - 1) ⇒ y = (-2/3)x + 2/3 + 3 ⇒ y = (-2/3)x + 11/3 

Thus, the equation of a secant line given two points (a, b) and (c, d) is y - b = [(d - b)/(c - a)] (x - a).