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

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 and then the equation of the line. The slope $m = \frac{46 - 60}{630 - 98} = \frac{-14}{532} = -\frac{1}{38}$. Using point-slope form, $y - y_1 = m(x - x_1)$, and choosing one of the points, for example, (98, 60), we can solve for the y-intercept (b). Substituting the slope and one point into the equation gives us the correct linear equation in the form $x = mp + b$, which matches choice C: $x = -\frac{1}{38}p + 62.58$.

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 $- \frac { 1 } { 38 }$