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 = $- \frac { 1 } { 38 }$ 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.
 
A)x = 532p + 62.58
B)x = -38p - 62.58
C)x = $- \frac { 1 } { 38 }$ p + 62.58
D)x = -38p + 62.58
E)x = 14p + 62.58

Quizplus · Accepted Answer

The relationship between rent (p) and demand (x) is linear, so we can use the two given points (98, 60) and (630, 46) to find the slope (m) of the line: $m = \frac{46 - 60}{630 - 98} = \frac{-14}{532} = -\frac{1}{38}$. Then, using point-slope form (y - y1 = m(x - x1)) with one of the points, we can find the equation of the line. Substituting $m = -\frac{1}{38}$ and using the point (98, 60), we get $x - 60 = -\frac{1}{38}(p - 98)$. Solving for x gives the equation $x = -\frac{1}{38}p + 62.58$, which matches choice C.

A Real Estate Office Handles an Apartment Complex with 60 −138- \frac { 1 } { 38 }−381​

A Real Estate Office Handles an Apartment Complex with 60 $- \frac { 1 } { 38 }$