https://file.aiquickdraw.com/mathbot/file/1727302952903dl9oct68.jpg

The problem is asking to compare two slope triangles in the image and explain why they both have the same slope.

### Let's break it down:

1. **Triangles in the Graph:**
   - The two right triangles share the same hypotenuse (the slanted line in the graph).
   - The larger triangle has a vertical leg of 5 and a horizontal leg of 3.
   - The smaller triangle has a vertical leg of 3 and a horizontal leg of 2.

2. **Slope Calculation:**
   - The slope of a line is calculated as **"rise over run"**, or the change in \( y \) (vertical) divided by the change in \( x \) (horizontal).
   - For the larger triangle, the slope is \( \frac{5}{3} \).
   - For the smaller triangle, the slope is \( \frac{3}{2} \).

3. **Why They Have the Same Slope:**
   - Both triangles lie on the same line, and since the slope of a line is constant along its entire length, the slope of both triangles must be the same.
   - The triangles are proportional, meaning that the ratio of their corresponding sides (the rise and run) is constant. This proportionality ensures that the slope of both triangles is equal.

Therefore, both triangles have the same slope because they are on the same line and the ratio between their vertical and horizontal sides (rise/run) remains constant along that line.

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Would you like further details on slope or help with another part? 

Here are 5 related questions:
1. How can you verify that two triangles are proportional?
2. What is the formula for slope in terms of coordinates?
3. Can two different lines have the same slope? If so, under what conditions?
4. How do you find the slope of a line when given its equation?
5. What happens to the slope if the line is vertical or horizontal?

**Tip:** Always remember that the slope of a line is constant no matter which points or triangles you use along the line.

Compare these triangles. Explain why they both have the same slope.

Learn how to compare slope triangles and understand why they have the same slope. This exercise explores the concept of slope, rise over run, and proportional triangles, suitable for students in grades 6-8.

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