Question

For the data in the table, does y vary directly with x?

X: 2 4 6
Y: 10 24 36

A. yes; y = 2x
B. yes; y = 5x
C. yes; y = 7x
D. no; y does not vary directly with x

Answer 1

After calculating the ratio of y to x for each pair and observing that the ratio is not constant, we can conclude that y does not vary directly with x, making option D the correct answer.

Step-by-step explanation:

The student has asked if y varies directly with x given the pairs of values for x and y. To determine if y is directly proportional to x, we must check if the ratio of y to x is consistent across all pairs. Checking each pair:

• When x = 2, y = 10, so y/x = 10/2 = 5.
• When x = 4, y = 24, so y/x = 24/4 = 6.
• When x = 6, y = 36, so y/x = 36/6 = 6.

The ratio of y to x is not constant because it changes from 5 to 6. Therefore, y does not vary directly with x, which means the correct answer is D. no; y does not vary directly with x.