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

Question

x y
8 11
16 22
24 33
(1 point)
Responses

yes; y = 2.75x
yes; y = 2.75 x

yes; y = 0.6875x
yes; y = 0.6875 x

yes; y = 1.375x
yes; y = 1.375 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 ratios of y and x are constant.

To find the ratios of y and x for the given data, we can divide each y value by its corresponding x value:

For the first set of data:
y/x = 11/8 ≈ 1.375

For the second set of data:
y/x = 22/16 ≈ 1.375

For the third set of data:
y/x = 33/24 ≈ 1.375

Since the ratios are all approximately equal (1.375), we can conclude that y varies directly with x.

Therefore, the correct equation for the direct variation is:
yes; y = 1.375x