Question

which is steeper a hill that rises 2 feet for every 10 feet of run, or a hill that rises 2 feet for every 15 feet of run? Explain

Answer 1

In order to figure this out you need to use slope intercept for for each of these hills. Let's say the first hill is HA and the second hill is B

slope intercept: y = mx + b

HA: y = (2/10)x
HB: y = (2/15)x

As you can see when you plot this on a graph, HB is steeper because the line rises more sharply.

Answer 2

Answer: Ok, the first hill rises 2 feet for every 10 feet of run.

So if both hills start in the ground where y = 0, we can write the height as a function of x in the next way: y = (2/10)*X so for every 10 feet you advance in x, you rise 2 feet in Y, where here 2/10 is the slope.

The second hill is described by y = (2/15)*X, so for every 15 feet in x, you rise 2 feet in y, and the slope is 2/15

Is easy to see that 2/10 > 2/15, so the slope of the first hill is bigger than the slope of the second hill, this means that the first hill is steeper than the second.