SAT Mathematics Practice Test 5

The linear function that represents the relationship will be in the form r(p)=ap+b, where a and b are constants and r(p) is the monthly rental price, in dollars, of a property that was purchased with p thousands of dollars. According to the table,(70,515) and (450,3,365) are ordered pairs that should satisfy the function, which leads to the system of equations below.
{

70a+b=515

450a+b=3,365

Subtracting side by side the first equation from the second eliminates b and gives 380a=2,850; solving for a gives a=

2,850

380

=7.5.Substituting 7.5 for a in the first equation of the system gives525+b=515; solving for b gives b=−10. Therefore, the linear function that represents the relationship is r(p)=7.5p−10.
Choices A, B, and C are incorrect because the coefficient of p, or the rate at which the rental price, in dollars, increasesfor every thousand-dollar increase of the purchase price is different from what is suggested by these choices. For example, the Glenview Street property was purchased for 140,000dollars, but the rental price that each of the functions in these choicesprovides is significantly off from the rental price given in the table, 1,040dollars.