Question
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.
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.
Answers
GPT-4o mini
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.**
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.**