calculus word problem!

Question

In May 1991, Car and Driver described a Jaguar that sold for 980,000 dollars. Suppose that at that price only 50 have been sold. If it is estimated that 300 could have been sold if the price had been 530,000 dollars. Assuming that the demand curve is a straight line, and that 530,000 dollars and 300 are the equilibrium price and quantity, find the consumer surplus at the equilibrium price.

Answer 1

(530-980)/(300-50)

-450/250=- 9/5= slope

P=-9x/5 +b is the demand curve

530=-9(300)/5+b

b= 530+9(60)= $1,070,000=price when no one buys the car

CS= (1/2)(300)(1070-530) in thousands= 150(540)= 81,000

$81,000,000 = Consumer Surplus at the equilibrium price

= the area of a triangle with base= 300, height = 540

=(1/2)(300)(540)=area above the price line P=530,000 and below the demand curve