Answer
$y=-\dfrac{1}{2}x+\dfrac{5}{2}$
Work Step by Step
You are given $(1,-2)$ and a perpendicular equation of $y=5x+4$.
Since the lines are perpendicular, the slope of the new equation is an opposite reciprocal so the slope $5$ would become $-\dfrac{1}{5}$.
Plug in the points to find B:
$y=-\dfrac{1}{5}x+b$
$-2=-\dfrac{1}{5}+b$
$b=\dfrac{5}{2}$
The new equation is $y=-\dfrac{1}{2}x+\dfrac{5}{2}$
