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The problem is asking which proportion can be used to show that the slope of segment \( JK \) is equal to the slope of segment \( MP \). Here's the process to find the correct proportion:

1. **Slope Formula**: The slope of a line segment is calculated as:
   \[
   \text{slope} = \frac{\text{change in y}}{\text{change in x}} = \frac{y_2 - y_1}{x_2 - x_1}
   \]

2. **Find the coordinates**:
   - Segment \( JK \): 
     - \( J = (-7, 0) \) and \( K = (-4, 4) \)
     - Slope of \( JK = \frac{4 - 0}{-4 - (-7)} = \frac{4}{3} \)
     
   - Segment \( MP \): 
     - \( M = (-10, 8) \) and \( P = (-1, -4) \)
     - Slope of \( MP = \frac{-4 - 8}{-1 - (-10)} = \frac{-12}{9} = \frac{-4}{3} \)

3. **Determine proportionality**: Since the slopes should be equal, we look for the option that matches these proportions.

Now, let’s analyze the answer choices:
- \( F: \frac{0 - (-7)}{4 - (-4)} = \frac{-4 - (-10)}{8 - (-1)} \)
- \( G: \frac{0 - 4}{-4 - (-7)} = \frac{-4 - 8}{-1 - (-10)} \)
- \( H: \frac{0 - (-4)}{4 - (-7)} = \frac{-4 - (-1)}{8 - (-10)} \)
- \( J: \frac{-4 - (-7)}{0 - 4} = \frac{-1 - (-10)}{-4 - 8} \)

Given that both slopes are \( \frac{-4}{3} \), the correct answer should represent this slope. Let's check **Option G**:
\[
G: \frac{0 - 4}{-4 - (-7)} = \frac{-4}{3} \quad \text{and} \quad \frac{-4 - 8}{-1 - (-10)} = \frac{-12}{9} = \frac{-4}{3}
\]
This is the correct proportion!

### The correct answer is **G**.

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Would you like more details or have further questions? Here are some related questions for further practice:

1. How do you calculate the slope between two points on a graph?
2. What are similar triangles, and how are their slopes related?
3. Can two lines have different slopes and still be part of similar triangles?
4. What role do negative signs play in interpreting slopes?
5. How would you verify the proportionality between two segments on a graph?

**Tip:** When working with slopes, always pay attention to the signs of both the rise (change in \( y \)) and the run (change in \( x \)) to avoid calculation errors.

Which proportion can be used to show that the slope of JL is equal to the slope of MP?

Explore how to use proportions to prove the slopes of line segments JL and MP are equal in similar right triangles. This problem involves calculating slopes and analyzing proportional relationships. Suitable for Grades 8-10.

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