Slope A descends15 vertical feet for every 24 horizontal feet

Question

Slopes descends 12 vertical feet for every 16 horizontal feet
Which is the steeper hill

Answer 1

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.

Answer 2

Does slope B have a smaller rate of change or a greater rate of change

Answer 3

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.