Question

"Is there a proportional relationship between Category 1 and Category 2 in the table below? Explain your answer.

Category 1 | 3 | 5
Category 2 | 15 | 20 | 25 | 30

A) Yes, there is a proportional relationship because Category 2 is always three times Category 1.
B) No, there is no proportional relationship because Category 2 does not vary linearly with Category 1.
C) Yes, there is a proportional relationship because Category 1 and Category 2 increase by the same amount.
D) No, there is no proportional relationship because Category 1 is always greater than Category 2."

Answer 1

The correct answer is B) No, there is no proportional relationship because Category 2 does not vary linearly with Category 1, as the ratio of the values is not consistent.

Step-by-step explanation:

To determine if there is a proportional relationship between Category 1 and Category 2 in the provided table, we need to check if the ratio of Category 2 to Category 1 is consistent across all pairs of values. A directly proportional relationship implies that as one quantity increases, the other increases at a constant rate, which can be represented by the equation y = kx, where k is the proportionality constant. In this case, if we divide the values in Category 2 by the corresponding values in Category 1, we see that 15/3 = 5, 20/5 = 4, 25 and 30 do not have corresponding values in Category 1 to test. Since the ratio is not consistent (5 and then 4), there is no proportional relationship between Category 1 and Category 2. Therefore, the correct answer would be B) No, there is no proportional relationship because Category 2 does not vary linearly with Category 1.