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 :)
