Find the revenue function R(p) for this hotel?

Question

A local hotel rented 450 rooms two nights ago when they charged $75 for each room. The following night they rented 600 rooms when they lowered the price to $60 per room. Assuming that this rate of change continues find the following:

 

Revenue is number of units rented times price per room. 

Answer 1

(450, 75), (600, 60)

slope = (75-60)/(450-600)= -1/10

P-60= (-1/10)(x-600)

P = -x/10 +120

R(x)= Px =(-1/10)x^2 +120x

or

10P-600 = -x + 600

x = -10P +1200

R(p) = Px = 1200P-10P^2