https://file.aiquickdraw.com/mathbot/file/1726456122127qre79txh.jpg

The problem asks to:

1. **Draw a secant line** on the graph of \( h(x) \).
2. **Determine the slope** of the secant line through the points where it crosses the graph.

### Step 1: Identify the points where the secant line crosses the graph
Looking at the image, we need to select two distinct points on the curve of \( h(x) \) to compute the secant line. From the graph, we can visually estimate the points where the secant line could cross.

- **First point (A)**: From the graph, one crossing point appears around \( A(-4, 0) \).
- **Second point (B)**: Another crossing point can be estimated near \( B(2, 4) \).

### Step 2: Calculate the slope of the secant line
The formula for the slope of a secant line between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Substituting the points \( A(-4, 0) \) and \( B(2, 4) \):

\[
\text{slope} = \frac{4 - 0}{2 - (-4)} = \frac{4}{2 + 4} = \frac{4}{6} = \frac{2}{3}
\]

Thus, the slope of the secant line is **\(\frac{2}{3}\)**.

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Would you like further details or clarification on the secant line and slope concept?

Here are 5 related questions to explore:
1. What is the difference between a secant line and a tangent line?
2. How would the slope change if the secant line passed through different points on the curve?
3. Can you calculate the equation of the secant line between the points found?
4. How can the slope of the secant line help approximate the slope of a tangent line?
5. What is the geometric meaning of the slope of a secant line in the context of functions?

### Tip:
When estimating points from a graph, try to use grid lines or scale markings to improve the accuracy of your estimates.

Draw a secant line on the graph of h(x), then determine the slope of the secant line through the points at which the secant line crosses h(x).

Learn how to draw a secant line on the graph of h(x) and determine the slope of the secant line using the slope formula. This problem includes identifying points from the graph and applying the formula to find the slope.

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