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 2 10 4 24 6 36 (1 point) Responses yes; y = 2x yes; y = 2 x yes; y = 5x yes; y = 5 x yes; y = 7x yes; y = 7 x no; y does not vary directly with x. no; y does not vary directly with x .
Answers
GPT 3.5
To determine if y varies directly with x, we can compare the ratios of y to x for each pair of values given in the table.
If the ratios are all equal, then y varies directly with x.
Let's calculate the ratios:
For the pair (2, 10): y/x = 10/2 = 5
For the pair (4, 24): y/x = 24/4 = 6
For the pair (6, 36): y/x = 36/6 = 6
Since the ratios are not equal for all pairs, y does not vary directly with x. Therefore, the correct response is:
no; y does not vary directly with x.
If the ratios are all equal, then y varies directly with x.
Let's calculate the ratios:
For the pair (2, 10): y/x = 10/2 = 5
For the pair (4, 24): y/x = 24/4 = 6
For the pair (6, 36): y/x = 36/6 = 6
Since the ratios are not equal for all pairs, y does not vary directly with x. Therefore, the correct response is:
no; y does not vary directly with x.