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.

1 answer

In order to determine if y varies directly with x, we need to check if the ratio of y to x is always the same. Let's calculate the ratios for each set of values:

y/x = 32/40 = 0.8
y/x = 16/28 = 0.5714
y/x = 12/16 = 0.75

The ratios are not all the same, so y does not vary directly with x. Therefore, the correct answer is:

no; y does not vary directly with x.