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

2x - 4y = 0

A.
yes; k = -4

B.
no

C.
yes; k = 1/2

D.
yes; k = -1/2

If expressed in terms of y ...

4y = 2x
y = (2/4)x = (1/2)x

so yes, with k = 1/2

To determine if the equation represents a direct variation, we need to check if it can be written in the form y = kx, where k is a constant.

Let's rearrange the equation 2x - 4y = 0.

Start by isolating y to one side of the equation:
-4y = -2x

Divide through by -4:
y = 1/2x

Comparing this with the form y = kx, we can see that the equation does represent a direct variation. Therefore, the correct answer is option C: yes, k = 1/2.

To determine if the equation represents a direct variation, we need to rewrite the equation in the form of y = kx. If the equation can be expressed in this form, where k is a constant, then it represents a direct variation.

Let's rearrange the given equation 2x - 4y = 0 to isolate y:

2x - 4y = 0
-4y = -2x
y = (2/4)x
y = (1/2)x

Now, we can see that the equation can be expressed as y = (1/2)x, where k = 1/2. This means that the equation represents a direct variation, where the constant of variation is k = 1/2.

Therefore, the correct answer is option C: yes; k = 1/2.