Question

For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation.

x

y

40

32

28

16

16

12

(1 point)
Responses

yes; y = 2x
yes; y = 2 x

yes; y = 0.5x
yes; y = 0.5 x

yes; y = 1.5x
yes; y = 1.5 x

no; y does not vary directly with x.
no; y does not vary directly with x.

Answer 1

To determine if y varies directly with x, we need to check if the ratio of y to x remains constant. Let's calculate the ratios for the given data:

32/40 = 0.8
16/28 = 0.57
12/16 = 0.75

Since the ratios are not all equal, we can conclude that y does not vary directly with x. Therefore, the correct answer is:

no; y does not vary directly with x.