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

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.

1 answer

To determine if y varies directly with x, we need to check if the ratio of y to x remains constant for the given values.

If we calculate the ratio of y to x for each pair of values, we get:

4/2 = 2
8/4 = 2
6/12 = 0.5
9/18 = 0.5
12/8 = 1.5
18/12 = 1.5

Since the ratio is the same for all pairs, we can conclude that y varies directly with x. So, the equation for the direct variation is: y = 2x.