Answer
$y = -\frac{1}{2}x + \frac{11}{2}$
Work Step by Step
For $y = 2x + 4$, the slope of it is 2 (by Slope-Intercept Form $y = mx + b)$.
For the slope of the line perpendicular to $y = 2x + 4$, it will be $- \frac{1}{2}$ (by $m_{1}m_{2} = -1)$.
Now, since the line perpendicular to $y = 2x + 4$ passes through $(1, 5)$, we have
$\frac{y - 5}{x - 1} = -\frac{1}{2}$
$2y - 10 = -x + 1$
$y = -\frac{1}{2}x + \frac{11}{2}$
