If Lindsey prefers to ski on a steeper hill, which should she choose, and why?

Question

slope A desencend 15 evertical feet for evrry 24 horzintal feet
slope B descends 12 vertical feet for every 16 horizontal feet

Slope B because it has a smaller rate of change.

Slope B because it has a greater rate of change.

Slope A because it has a greater rate of change.

Slope A because it has a smaller rate of change.

Answer 1

To determine which slope is steeper, we need to calculate the slope (or the rate of change) for both Slope A and Slope B.

Slope A:

• Vertical change: 15 feet
• Horizontal change: 24 feet

The slope (m) is calculated as: $$m=\frac{\text{vertical change}}{\text{horizontal change}}=\frac{15}{24}=\frac{5}{8}$$

Slope B:

• Vertical change: 12 feet
• Horizontal change: 16 feet

Similarly, the slope for B is: $$m=\frac{12}{16}=\frac{3}{4}$$

Now let's compare the two slopes:

• Slope A = 5/8 = 0.625
• Slope B = 3/4 = 0.75

Since 3/4 (or 0.75) is greater than 5/8 (or 0.625), Slope B is steeper than Slope A.

Therefore, the correct choice is:

Slope B because it has a greater rate of change.