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Question 70690This question is from textbook College Algebra
: 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 euqation of the line giving the demand (x) in terms of the rent (p).
This question is from textbook College Algebra
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 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
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