A transfer station charges $15 for a waste disposal permit and an additional $5 for each cubic yard of garbage it disposes of this relationship can be described using the expression 15+5x. What effect if any does changing the value of x have on the cost of the permit

Actually the given equation 15 + 5x is a linear equation. We can see that the equation is in the form of:

y = mx + b

where,

m = slope = 5

b = y intercept = 15

Since the slope is 5, therefore this means that changing the value of x by 1 changes the value of the cost of the permit by 5. So for every 1 change in x, there is a corresponding 5 change in the cost of the permit.