Question

If DVDs are on sale for $10.50 each, what is the rule for the amount y (in dollars) you spend as a function of the number x of DVDs you buy?

A. y = 10.50x
B. y = x - 10.50
C. y = 10.50 - x
D. y = 10.50 + x

Answer 1

The correct rule for the amount spent on DVDs at $10.50 each is represented by the function y = 10.50x, which describes a direct relationship between the number of DVDs purchased (x) and the total cost (y).

Step-by-step explanation:

If DVDs are on sale for $10.50 each, the rule for the amount y (in dollars) you spend as a function of the number x of DVDs you buy is y = 10.50x. This is because the total cost is directly proportional to the number of DVDs purchased. Every additional DVD adds another $10.50 to the total cost, which is a linear relationship.

We can disregard the other options because they either suggest that the cost decreases as more DVDs are bought (y = 10.50 - x), or they imply an incorrect relationship between the number of DVDs and the total cost. For instance, option B would mean you pay less for more DVDs, and option D implies an additional cost that doesn't depend on the number of DVDs. Neither of these reflect a direct and constant rate per DVD.