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To find the slope of the secant line, we need to use the slope formula between two points \( (x_1, y_1) \) and \( (x_2, y_2) \), which is given by:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Here, the two points given are \( (-2, f(-2)) \) and \( (4, f(4)) \). Let's extract the function values from the graph.

- At \( x = -2 \), it looks like \( f(-2) = -2 \).
- At \( x = 4 \), it looks like \( f(4) = 1 \).

So, the two points are \( (-2, -2) \) and \( (4, 1) \).

Now, applying the slope formula:

\[
m = \frac{1 - (-2)}{4 - (-2)} = \frac{1 + 2}{4 + 2} = \frac{3}{6} = \frac{1}{2}
\]

Thus, the slope of the secant line is \( \frac{1}{2} \).

Would you like more details on secant lines, or do you have any other questions?

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Here are five related questions you might explore:
1. How is the secant line different from a tangent line?
2. How does the slope of the secant line relate to the average rate of change of the function?
3. Can the slope of the secant line be used to estimate the derivative at a point?
4. How would you find the equation of the secant line itself?
5. How does the secant line's slope change if the interval between the points is smaller?

**Tip:** The slope of a secant line represents the average rate of change of the function between two points.

In the above graph of y = f(x), find the slope of the secant line through the points (-2, f(-2)) and (4, f(4)).

Learn how to find the slope of the secant line through two points on a graph, with specific points (-2, f(-2)) and (4, f(4)). This problem provides step-by-step instructions for using the slope formula to determine the average rate of change between two points on a curve.

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