Given the slope \( m = -2 \) and the y-intercept \( b = 4 \), we can substitute these values into the slope-intercept form of a linear equation, which is given by:
\[ y = mx + b \]
Substituting the values we have:
\[ y = -2x + 4 \]
So, the completed equation of the line is:
\[ y = -2x + 4 \]