Question 70690
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.
:
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) Write the equation of the line giving the demand (x) in terms of the rent (p)
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