For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation.
x y
4 28
6 48
8 72
A.yes; y = 2x
B.yes; y = 5x
C.yes; y = 7x
D.no; y does not vary directly with x. ***
To determine if y varies directly with x, we need to check if the ratio between y and x is constant for all values in the table. Let's calculate the ratios:
For the pairs (4, 28) and (6, 48):
28/4 = 7
48/6 = 8
For the pairs (6, 48) and (8, 72):
48/6 = 8
72/8 = 9
Since the ratios between y and x are not constant, y does not vary directly with x. Therefore, the correct answer is D) no; y does not vary directly with x.
To determine whether y varies directly with x, we need to check if the ratio of y to x remains constant for each pair of values in the table.
Let's calculate the ratios for the given data:
For the first pair (4, 28), the ratio of y to x is 28/4 = 7.
For the second pair (6, 48), the ratio of y to x is 48/6 = 8.
For the third pair (8, 72), the ratio of y to x is 72/8 = 9.
Since the ratios are not constant for each pair, we can conclude that y does not vary directly with x. Therefore, the correct answer is D. no; y does not vary directly with x.