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

Lindsey is practising her downhill skating.
Slope A descends 15 vertical feet for every 24 horizontal feet.
Slope B descends 12 vertical feet for every 16 horizontal feet.

Slope A because it has a greater rate of change.

Slope B because it has a greater rate of change.

Slope A because it has a smaller rate of change.

Slope B because it has a smaller rate of change.

1 answer

To determine which slope Lindsey should choose based on the steepness, we need to calculate the rate of change (slope) for both Slope A and Slope B.

The rate of change (slope) is given by the formula:

\[ \text{slope} = \frac{\text{vertical change}}{\text{horizontal change}} \]

For Slope A: \[ \text{slope A} = \frac{15 \text{ feet}}{24 \text{ feet}} = \frac{15}{24} = \frac{5}{8} = 0.625 \]

For Slope B: \[ \text{slope B} = \frac{12 \text{ feet}}{16 \text{ feet}} = \frac{12}{16} = \frac{3}{4} = 0.75 \]

Now, we compare the slopes:

  • Slope A: 0.625
  • Slope B: 0.75

Since Slope B has a greater rate of change (0.75 > 0.625), it is steeper than Slope A.

Therefore, Lindsey should choose Slope B because it has a greater rate of change.