Question

Do these pairs of values (x and y) represent two quantities that are

proportional?
X y
3 12
5 20
6 24
9 36
A. No, because none of the pairs is a simplified ratio.
B. Yes, because all of the pairs represent the same ratio.
C. No, because the y-values are not increasing at a constant rate.
O D. Yes, because as x increases, y increases.

Answer 1

After calculating the ratios for each pair of values (x, y), it is clear that all pairs have the constant ratio of 4, which means that x and y are directly proportional. The correct answer is B, as all of the pairs represent the same ratio.

Step-by-step explanation:

To determine if the pairs of values (x and y) represent two quantities that are proportional, we need to see if there's a constant ratio between them. For two values to be proportional, the ratio of y to x should be constant. Let's calculate the ratios:

• For (3, 12): 12 ÷ 3 = 4
• For (5, 20): 20 ÷ 5 = 4
• For (6, 24): 24 ÷ 6 = 4
• For (9, 36): 36 ÷ 9 = 4

Since all pairs have the same ratio of 4, we can conclude that the quantities x and y are directly proportional. The correct answer to the question is B. Yes, because all of the pairs represent the same ratio.