https://file.aiquickdraw.com/mathbot/file/1726184467567lhkv4pr3.jpg

To find the slope of the secant line through the points \((-4, f(-4))\) and \((3, f(3))\), we can apply the slope formula:

\[
m = \frac{f(3) - f(-4)}{3 - (-4)}
\]

Now, let's extract the \(y\)-coordinates (i.e., \(f(-4)\) and \(f(3)\)) from the graph:

- At \(x = -4\), the graph shows that \(f(-4) = -3\).
- At \(x = 3\), the graph shows that \(f(3) = 2\).

Now, substitute these values into the slope formula:

\[
m = \frac{2 - (-3)}{3 - (-4)} = \frac{2 + 3}{3 + 4} = \frac{5}{7}
\]

Thus, the slope of the secant line is:

\[
m = \frac{5}{7}
\]

Let me know if you'd like further details or if you have any questions!

### Related Questions:
1. How is the secant line different from the tangent line?
2. What does the slope of a secant line represent geometrically?
3. How can we find the average rate of change of the function over an interval?
4. What is the importance of secant lines in calculus?
5. How can you approximate a derivative using secant lines?

### Tip:
The secant line's slope can be interpreted as the average rate of change of the function over the interval between the two points.

In the above graph of y = f(x), find the slope of the secant line through the points (-4, f(-4)) and (3, f(3)).

Learn how to calculate the slope of a secant line through the points (-4, f(-4)) and (3, f(3)) using the slope formula. The graph gives f(-4) = -3 and f(3) = 2, making the slope m = 5/7. Ideal for high school students learning about functions and analytic geometry.

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