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.