Question

Luther wants to get in shape, so he joins a local gym, Buff and Tough. For membership, the gym charges a registration fee plus monthly dues. This table shows the relationship between the length of Luther's gym membership (in months), x, and the total cost of his membership (in dollars), y. x (months) y (dollars) 2 $49 3 $65 4 $81 5 $97 According to the values in the table, do x and y have a proportional relationship? yes no What is the constant of proportionality? Write your answer as a whole number or decimal. dollars per month

Answer 1

To determine if x and y have a proportional relationship, we can check if the ratio between the values of x and y remains constant.

Using the given table:

For x = 2, y = $49 For x = 3, y = $65 For x = 4, y = $81 For x = 5, y = $97

Let's calculate the ratios:

Ratio between y and x for x = 2: 49/2 = 24.5 Ratio between y and x for x = 3: 65/3 = 21.67 Ratio between y and x for x = 4: 81/4 = 20.25 Ratio between y and x for x = 5: 97/5 = 19.4

Since the ratios are not constant, x and y do not have a proportional relationship. Therefore, there is no constant of proportionality.