What is the slope of the secant line between the points (af(a)) and (b,f(b)) on the graph of f?
Which of the following is the correct formula for the slope of the secant line?

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.

What is the slope of the secant line between the points (a, f(a)) and (b, f(b)) on the graph of f? Which of the following is the correct formula for the slope of the secant line?

Understand how to calculate the slope of a secant line between two points (a, f(a)) and (b, f(b)) on the graph of a function f. This tutorial covers essential algebra and calculus concepts, including the formula for the slope of a secant line and its relation to the average rate of change. Ideal for students in Grades 10-12.

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