The slope of two perpendicular lines, when multiplied becomes \(-1\).

The given line : \(y = 2x + 4\)
When we compare it to \(y = mx + c\), the slope \(m = 2\)

So the line that is perpendicular will have a slope of \(-\frac{1}{2}\)

Let's convert all the options in the form of \(y = mx + c\)

A. 2y+x=5 :: \(y = \frac{-x}{2} + \frac{5}{2}\)

B. 2y-x=3 :: \(y = \frac{x}{2} + \frac{3}{2}\)

C. x+2y=7 :: \(y = \frac{-x}{2} + \frac{7}{2}\)

D. x-2y=4 :: \(y = \frac{x}{4} + -2\)

E. 4y+2x=0 :: \(y = \frac{-x}{2} \)

Answer A C E