The slope of the secant line between the points $(a, f(a))$ and $(b, f(b))$ on the graph of the function $f$ is given by the difference in the $y$-coordinates divided by the difference in the $x$-coordinates. This is mathematically expressed as:

$\text{Slope of secant line} = \frac{f(b) - f(a)}{b - a}$

This formula represents the average rate of change of the function $f(x)$ between the points $x = a$ and $x = b$.

Summary

• Formula: $\frac{f(b) - f(a)}{b - a}$

Do you have any questions or need further details on this?

Here are 5 related questions for further exploration:

1. What is the difference between the slope of a secant line and the slope of a tangent line?
2. How does the slope of the secant line relate to the average rate of change of a function?
3. How would the slope of the secant line change if $a = b$?
4. Can the slope of a secant line be used to estimate the slope of a tangent line at a point?
5. How does the slope of the secant line change as the points $a$ and $b$ get closer together?

Tip: The slope of the secant line provides a good approximation of the derivative (slope of the tangent line) as the points $a$ and $b$ get closer.