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.

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x