Answer
The new equation is $y=-\dfrac{1}{5}x-\dfrac{9}{5}$
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:
$y=-\dfrac{1}{5}x+b$
$-2=-\dfrac{1}{5}+b$
$b=-\dfrac{9}{5}$
The new equation is $y=-\dfrac{1}{5}x-\dfrac{9}{5}$
