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

Question

A. yes; y = 2x yes;
b. y = 0.5x yes;
c. y = 1.5x yes;
d. y does not vary directly with x.

Answer 1

In order to determine if y varies directly with x, we need to check if the ratio of y to x is constant for all the given data points.

Let's calculate the ratios for each pair of corresponding values from the table:
For the first pair (1, 2): y/x = 2/1 = 2
For the second pair (2, 4): y/x = 4/2 = 2
For the third pair (3, 6): y/x = 6/3 = 2
For the fourth pair (4, 8): y/x = 8/4 = 2

Since the ratio of y to x is always 2 for all data points, we can conclude that y varies directly with x.

Therefore, the correct choice is:
A. yes; y = 2x