A real estate office handles an apartment complex with 70 units. When the rent is $405 per month, all 70 units are occupied. When the rent is $450, however, the average number of occupied units drops to 67. Assume that the relationship between the monthly rent p and the demand x is linear. (The term demand refers to the number of occupied units.) (a) Write a linear equation expressing x in terms of p.x = (b) Predict the number of occupied units when the rent is set at $480.(c) Predict the number of occupied units when the rent is set at $435.

x = 70-(p-405)/15

(p, x) -> Points: (405, 70)(450, 67)x = # of unitsp = cost of rentm = (67 - 70) / (450 - 405) = -1/15Using point slope formula, y = (x - h) + k:x = -1/15(p - 405) + 70x = -(1/15)p + 27 + 70x = -(1/15)p + 97b) x = -(1/15)(480) + 97x = 65 unitsc) x = -(1/15)(435) + 97x = 68 units

more the rent lesser the number of occupied houses or p inversely propotional to x or p=k/x +C (k,C are constant)thus 405=k/70+C and 450=k/67+Cfrom these two equations 45=k(1/67-1/70) or k=70350so from first equation C=405-70350/70=-600so equation is p=70350/x-600Rest can be calculated from equation