A piece of climbing equipment at a playground is 6 feet high and extends 4 feet horizontally. A piece of climbing equipment at a gym is 10 feet high and extends 6 feet horizontally. Which statement best compares the slopes of the two pieces of equipment? Because \( \frac{5}{3}>\frac{3}{2} \), the slope of the climbing equipment at the gym is greater. Because \( \frac{5}{3}<\frac{3}{2} \), the slope of the climbing equipment at the playground is greater. Because \( \frac{3}{5}>\frac{2}{3} \), the slope of the climbing equipment at the gym is greater. Because \( \frac{3}{5}<\frac{2}{3} \), the slope of the climbing equipment at the playground is greater.

To compare the slopes of the two pieces of climbing equipment, we calculate the slope using the formula for slope, which is rise over run. For the playground equipment, the rise is 6 feet and the run is 4 feet, giving us a slope of \( \frac{6}{4} = \frac{3}{2} \). For the gym equipment, the rise is 10 feet and the run is 6 feet, resulting in a slope of \( \frac{10}{6} = \frac{5}{3} \). Since \( \frac{5}{3} > \frac{3}{2} \), the slope of the climbing equipment at the gym is, in fact, greater! How about this for a fun scenario: Imagine you and a friend are scaling these two climbing structures. In the playground, as you climb that 6-foot-high structure, the view is charming but slightly less exhilarating. Then, transitioning to the gym's 10-foot height, you get a rush of adrenaline! It's not just about who's higher, but also the angle—steeper slopes mean more thrill on the way up (and possibly on the way down too!).