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
A. yes; y = 2x
B. yes; y = 0.5
C. yes; y = 1.5x
D. no; y does not vary directly with x.
To determine if y varies directly with x, we need to check if the ratio of y to x remains constant for all values.
Using the given data, let's calculate the ratios of y to x:
For the first pair (40, 32): y/x = 32/40 = 0.8
For the second pair (28, 16): y/x = 16/28 ≈ 0.571
For the third pair (16, 12): y/x = 12/16 = 0.75
The ratio of y to x is not constant for all values, meaning that y does not vary directly with x. Therefore, the answer is D. no; y does not vary directly with x.