A real estate office handles an apartment complex with 60 units.When the rent per unit is $98 per month, all 60 units are occupied.However, when the rent is $630 per month, the average number of occupied units drops to 46.Assume that the relationship between the monthly rent p and the demand x is linear. Select the equation of the line giving the demand x in terms of the rent p.

A)x = 532p + 62.58
B)x = -38p - 62.58
C)x = p + 62.58
D)x = -38p + 62.58
E)x = 14p + 62.58

Question

A real estate office handles an apartment complex with 60 units.When the rent per unit is $98 per month, all 60 units are occupied.However, when the rent is $630 per month, the average number of occupied units drops to 46.Assume that the relationship between the monthly rent p and the demand x is linear. Select the equation of the line giving the demand x in terms of the rent p.
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A)x = 532p + 62.58 
B)x = -38p - 62.58 
C)x = p + 62.58 
D)x = -38p + 62.58 
E)x = 14p + 62.58

Quizplus · Accepted Answer

We can assume a linear equation of the form x = mp + b, where m is the slope and b is the y-intercept. 
When the rent is $98 per month, all 60 units are occupied. This gives us the point (98,60). 
When the rent is $630 per month, the average number of occupied units drops to 46. This gives us another point (630,46). 
Using these two points, we can find the slope:

m = (46 - 60) / (630 - 98) = -14/133

To find the y-intercept, we can plug in one of the points and solve for b:

60 = (-14/133)(98) + b 
b = 62.58

Therefore, the equation of the line is x = (-14/133)p + 62.58, which simplifies to:

x = 0.1043p + 62.58

This is closest to choice (C), x = 11eacce6_21cd_04ca_9f49_3796f5971bff_TB7896_11p + 62.58 when rounded to the nearest ten-thousandth.

A Real Estate Office Handles an Apartment Complex with 60