To compare the slopes of the two pieces of climbing equipment, we first need to calculate the slopes for each.
1. Calculate the slope of the playground equipment:
The slope is calculated by dividing the vertical height by the horizontal distance.
- Vertical height of playground equipment [tex]\( = 6 \)[/tex] feet
- Horizontal distance of playground equipment [tex]\( = 4 \)[/tex] feet
The slope is:
[tex]\[
\text{slope}_{\text{playground}} = \frac{6}{4} = 1.5
\][/tex]
2. Calculate the slope of the gym equipment:
Similarly, the slope for the gym equipment is calculated by dividing the vertical height by the horizontal distance.
- Vertical height of gym equipment [tex]\( = 10 \)[/tex] feet
- Horizontal distance of gym equipment [tex]\( = 6 \)[/tex] feet
The slope is:
[tex]\[
\text{slope}_{\text{gym}} = \frac{10}{6} \approx 1.6667
\][/tex]
3. Compare the slopes:
Now we compare the calculated slopes:
- Slope of the playground equipment [tex]\( = 1.5 \)[/tex]
- Slope of the gym equipment [tex]\( \approx 1.6667 \)[/tex]
Since:
[tex]\[
1.6667 > 1.5
\][/tex]
The slope of the gym equipment is greater than the slope of the playground equipment.
Therefore, the correct statement that best compares the slopes is:
[tex]\[
\text{Because } \frac{5}{3} > \frac{3}{2}, \text{ the slope of the climbing equipment at the gym is greater.}
\][/tex]
