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 [tex]y = x * (constant)[/tex].
In answer a, [tex]y = x*.5[/tex], so it is a direct variation.
In answer c, [tex]y = x* \frac{1}{9} [/tex], so it is a direct variation.
In answer d, [tex]y = x*2[/tex], 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 [tex]y = x * (constant)[/tex]. Instead, it is expressed as [tex]y = \frac{constant}{x} [/tex], 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 :)
