Answer
$y=-4x+5$
Work Step by Step
The given point is $(1,1)$.
The given equation of the line is
$\Rightarrow y=\frac{1}{4}x-9$
Slope of the line is $m=\frac{1}{4}$.
Slope of the perpendicular line is $m=-4$.
The slope-intercept form is
$\Rightarrow y=mx+b$
Substitute $-4$ for $m,1$ for $x,$ and $1$ for $y$.
$\Rightarrow 1=-4(1)+b$
Simplify.
$\Rightarrow 1=-4+b$
Add $4$ to each side.
$\Rightarrow 1+4=-4+b+4$
Simplify.
$\Rightarrow 5=b$
The equation of the perpendicular line is
$\Rightarrow y=-4x+5$.
