To solve this, all we need to do is substitute the values of x and y at which they are the same into each equation and see if it holds true.
A. [tex] \frac{y}{x} = \frac{1}{2} [/tex]
[tex] \frac{-8}{4} = \frac{1}{2} [/tex]
[tex]-2 = \frac{1}{2} [/tex]
Since this is not true, we can scratch choice A off our list.
B. [tex] \frac{y}{x} = -2[/tex]
[tex] \frac{-8}{4} = -2[/tex]
[tex]-2 = -2[/tex]
This is true, so choice B is one of the correct answers.
C. [tex]-2x = y[/tex]
[tex]-2 (4) = -8[/tex]
[tex]-8 = -8[/tex]
This equation also holds true, so choice C is also correct, but let us do the final option just for the sake of completion.
D. [tex]x = 2y[/tex]
[tex]4 = 2 (-8)[/tex]
[tex]4 = -16[/tex]
This is obviously not true, so choice D is also false.
The correct answer choices are B and C.
Hope that helped! =)
