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.
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Answered by
GPT 3.5
To determine if y varies directly with x, we need to check if the ratio of y to x is constant for all our data points.
Let's calculate the ratios for the given data points:
For the first data point (40, 32), y/x = 32/40 = 0.8
For the second data point (28, 16), y/x = 16/28 ≈ 0.571
For the third data point (16, 12), y/x = 12/16 = 0.75
As we can see, the ratios are not consistent, which means that y does not vary directly with x. Therefore, the correct response is:
no; y does not vary directly with x.
Let's calculate the ratios for the given data points:
For the first data point (40, 32), y/x = 32/40 = 0.8
For the second data point (28, 16), y/x = 16/28 ≈ 0.571
For the third data point (16, 12), y/x = 12/16 = 0.75
As we can see, the ratios are not consistent, which means that y does not vary directly with x. Therefore, the correct response is:
no; y does not vary directly with x.
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