Question

the top and bottom of a slide are parallel to the ground. what is the slope of the main portion of the slide? how does the slope change if the bottom is lowered to 15 inches off the ground and width extended to 13 feet (steeper or less steep)? explain if the “new” slide would be steeper or less steep than the “old” slide. explain here.

Explanation:

Step1: Calculate old vertical rise

Total height: 8 ft; bottom height: 18 in = 1.5 ft. Rise = 8 - 1.5 = 6.5 ft.

Step2: Old slope (rise/run)

Run = 12 ft. Slope = $\frac{6.5}{12} \approx 0.542$.

Step3: New vertical rise

New bottom height: 15 in = 1.25 ft. New rise = 8 - 1.25 = 6.75 ft.

Step4: New slope (rise/run)

New run = 13 ft. Slope = $\frac{6.75}{13} \approx 0.519$.

Step5: Compare slopes

0.519 < 0.542, so new slope is less steep.

Answer:

The slope of the main portion of the old slide is approximately 0.54. The new slide would be less steep than the old slide because the new slope (≈0.519) is smaller than the old slope (≈0.542).