Question

Which does not show a direct variation between x and y?

Answer 1

A direct variation is a mathematical relationship between two variables that can be expressed by an equation in which one variable is equal to a constant times the other. In other words, a direct variation is where $y = x * (constant)$.

In answer a, $y = x*.5$, so it is a direct variation.
In answer c, $y = x* \frac{1}{9}$, so it is a direct variation.
In answer d, $y = x*2$, so it is a direct variation,

Only answer b is left, which means the answer must be 'b'. 

We also know 'b' is the answer because it cannot be expressed as $y = x * (constant)$. Instead, it is expressed as $y = \frac{constant}{x}$, which is not the same thing and is therefore not a direct variation.

Hope I helped, and let me know if you have any questions :)

Answer 2

A relationship between two variables in which one is a constant multiple of the other. In particular, when one variable changes the other changes in proportion to the first. If b is directly proportional to a, the equation is of the form b = ka (where k is a constant).
B.y = 9/x