Question

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

A.
y = 0.5x

B.
y = 9/x

C.
y = x/9

D.
y = 2x

Answer 1

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

Answer 2

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* (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 = (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 :)