Let's solve the equation \(-x = 8 - 4y\) for \(y\) and see if we can express it in the form \(y = \frac{1}{4}x + 2\).
Starting with the original equation:
\[ -x = 8 - 4y \]
We can rearrange it to isolate \(y\). First, let's add \(4y\) to both sides:
\[ -x + 4y = 8 \]
Next, we can add \(x\) to both sides:
\[ 4y = x + 8 \]
Now, divide both sides by 4 to solve for \(y\):
\[ y = \frac{1}{4}x + 2 \]
So the equation \(y = \frac{1}{4}x + 2\) is indeed the correct solution to the original equation \(-x = 8 - 4y\).