A real estate office handles an apartment complex with 50 units. When the rent per unit is $580 per month, all 50 units are occupied. However, when the rent is $625 per month, the average number of occupied units drops to 47. Assume that the relationship between the monthly rent p and the demand x is linear.

Question

A real estate office handles an apartment complex with 50 units. When the rent per unit is $580 per month, all 50 units are occupied. However, when the rent is $625 per month, 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 the equation of the line giving the demand x in terms of the rent p.
x =

(b) Use this equation to predict the number of units occupied when the rent is $640.
 units

(c) Predict the number of units occupied when the rent is $595.
 units

Study Question · Answer

Since the equation will be linear, we only need two coordinates to write the equation.
They are given, we can assign the values x = no. of units and y = rent:
x1 = 50, y1 = 580 and x2 = 47, y2 = 625

Find the slope: m = (y2-y1)/(x2-x1)
m = (625-580)/(47 - 50) = 45/-3 = -15 is the slope (m)

a)
Use the point/slope equation

Using the point/slope formula: y - y1 = m(x - x1)
y - 580 = -15(x - 50)
y - 580 = -15x + 750
y = -15x + 750 + 580
y = -15x + 1330 or p(x) = -15x + 1330