Does the equation represent a direct variation? If so, find the constant of variation.

2x - 4y = 0

A. yes; k = 1/2

B. no

C.

yes; k = - 4

D. yes; k = - 1/2

We are given the equation that represents a direct variation 2x - 4y = 0.

We know direct variation equation y = k x.

Where x is the constant of variation.

In order to find if given equation is really a direct variation, we need to solve it for y.

2x - 4y = 0

Subtracting 2x from both sides, we get

-4y = - 2x.

Dividing both sides by 4, we get

y = 1/2 x.

On comparing with direct variation equation y = k x. We can see that y = 1/2 x is also a direct variation equation.

And k = 1/2.

Therefore, correct option is A. Yes; k = 1/2.