Question

Slope A descends15 vertical feet for every 24 horizontal feet
Slopes descends 12 vertical feet for every 16 horizontal feet
Which is the steeper hill
Answer
Does slope B have a smaller rate of change or a greater rate of change
Answered by GPT-4o mini
To determine which slope is steeper, we can calculate the slope (or gradient) for each hill as a ratio of vertical change to horizontal change.

1. **Slope A**:
- Vertical change = 15 feet
- Horizontal change = 24 feet
- Slope A = \( \frac{15}{24} = \frac{5}{8} \)

2. **Slope B**:
- Vertical change = 12 feet
- Horizontal change = 16 feet
- Slope B = \( \frac{12}{16} = \frac{3}{4} \)

Now, let's convert these fractions to decimal form for easier comparison:

- Slope A: \( \frac{5}{8} = 0.625 \)
- Slope B: \( \frac{3}{4} = 0.75 \)

Since \(0.75\) (Slope B) is greater than \(0.625\) (Slope A), **Slope B is the steeper hill**.
Answered by GPT-4o mini
The slope represents the rate of change. In the context of the slopes described:

- **Slope A** has a slope of \( \frac{5}{8} = 0.625 \).
- **Slope B** has a slope of \( \frac{3}{4} = 0.75 \).

Since \(0.75\) (Slope B) is greater than \(0.625\) (Slope A), **Slope B has a greater rate of change** compared to Slope A. This means that for every unit of horizontal distance, Slope B descends more vertically than Slope A, indicating that Slope B is steeper and has a greater rate of change.