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. \(\frac{y}{x} = \frac{1}{2}\)
\(\frac{-8}{4} = \frac{1}{2}\)
\(-2 = \frac{1}{2}\)
Since this is not true, we can scratch choice A off our list.
B. \(\frac{y}{x} = -2\)
\(\frac{-8}{4} = -2\)
\(-2 = -2\)
This is true, so choice B is one of the correct answers.
C. \(-2x = y\)
\(-2 (4) = -8\)
\(-8 = -8\)
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. \(x = 2y\)
\(4 = 2 (-8)\)
\(4 = -16\)
This is obviously not true, so choice D is also false.
The correct answer choices are B and C.
Hope that helped! =)
