A real estate office manages an apartment complex with 50 units. When the rent is $780 per month, all 50 units are occupied. However, when the rent is $825, the average number of occupied units drops to 47. Assume that the relationship between the monthly rent p and the demand x is linear. 

(a) Write a linear equation giving the demand x in terms of the rent p.

(b) Linear extrapolation Use a graphing utility to graph the demand equation and use the trace feature to predict the number of units occupied when the rent is raised to $855.

(c) Linear interpolation Predict the number of units occupied
when the rent is lowered to $795. Verify graphically.