In the equation \( 4x = -y \), we can rewrite it in the standard form for direct variation, which usually takes the form \( y = kx \), where \( k \) is the constant of variation.
To express \( y \) in terms of \( x \):
\[ y = -4x \]
From this, we can identify that the constant of variation \( k \) is:
\[ k = -4 \]
Therefore, the constant of variation \( k \) for the direct variation represented by the equation \( 4x = -y \) is \( -4 \).