For the data in the table below, does y vary directly with x? if it does, write an equation for the direct variation. x} 1 3 7 y } 3 7 15

No, y does not vary directly with x.

Justification:

When a variable varies directly with other it me
ans that one is the other times a constant. This is y = k * x, which implies y / x = k.

So, lets determine whether the data meet that y / x = k.

1) y = 3, x = 21 => y / x = 3

2) y = 7, x = 3 => y / x = 7/3 ≠ 3 => y / x is not a constant.

Note that direct variation is the same that directly proportional but not the same that linear variation. Just in case you have some confussion.

With that you have already proved that for the data y does not vary directly with x.

Let's do the same for the third pair, just for exercise:

3) y = 15, x = 7 => y / x = 15 / 7 ≈≠ 3 and 15 / 7 ≠ 7/3. This pair also proves that the relation is not direct.