The distance a spring will stretch varies directly with how much weight is attached to the spring. if a spring stretches 5 inches with 50 pounds attached, how far will it stretch with 170 pounds attached?

There is a few ways to do this but I am going to use the variation equation.

Variation Equation:
y = kx
First we need to find k, which is the constant of variation
5 = k50
5/50 = k
1/10 = k
k= 1/10

Now that we have found the constant of variation, we can find how much the spring will stretch with 170 pounds.
y = kx
y = (1/10) times 170 = 17 inches