How to Find the Slope of a Secant Line: A Quick Guide

Calculate the slope of a secant

Written by Kyle Smith

Last Updated: February 20, 2023

Calculating the secant line is easy! Use the slope formula for two points to find it. This wikiHow guide shows you how to find the slope of a secant line.

Things You Should Know

Identify the two points where the secant line intersects f(x).
Insert the points (x1, y1) and (x2, y2) into the slope equation.
The slope equation is $m={\frac {y_{2}-y_{1}}{x_{2}-x_{1}}}$

Steps

1
Identify the two points. The secant line intersects two points on your curve f(x). Find the coordinates for those two points.^{[1]
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- This might be given to you in the general form of (x1, y1) and (x2, y2)
- If you only have the equation for f(x) and the secant line, plug in the two x values (x1 and x2) into f(x) to get y1 and y2 respectively.
2
Insert the points into the slope equation. The slope of the secant line is the average rate of change for your curve over an interval. To calculate the slope (m) of a line, use the equation:
- $m={\frac {y_{2}-y_{1}}{x_{2}-x_{1}}}$
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3
Consider this example. If you have two points (3, 6) and (5, 7) defining a secant line, plug them into the slope equation:
- $m={\frac {7-6}{5-3}}$
- $m=0.5$