Question

a gym charges a one time fee of $50 and monthly membership charge of $25 the total cost c of being a member of the gym is given by c (t)=50+25t,where c is the total cost you pay after being a member for t months

Answer 1

C(t) = 50 + 25t 
A) So $50 was a one time pay and that's your initial value and each month they need to pay $25. So the slope is 50 
B) the y-int of your problem is $50  

Answer 2

A. The slope is 25 and it is the rate of change per month. You will pay this additional amount if you go to the gym every month.
b. The y-intercept is 50. This amount is the constant and does not change since it is a one time fee for the year.