Answer
The equation of the perpendicular line is
$y=\frac{1}{2}x-3$.
Work Step by Step
The given point is $(8,1)$.
The given equation of the line is
$\Rightarrow 2y+4x=12$
Slope-intercept form is
$\Rightarrow y=-2x+6$
Slope of the line is $m=-2$.
Slope of the perpendicular line is $m=\frac{1}{2}$.
The slope-intercept form is
$\Rightarrow y=mx+b$
Substitute $\frac{1}{2}$ for $m,8$ for $x,$ and $1$ for $y$.
$\Rightarrow 1=\frac{1}{2}(8)+b$
Simplify.
$\Rightarrow 1=4+b$
Subtract $4$ from each side.
$\Rightarrow 1-4=4+b-4$
Simplify.
$\Rightarrow -3=b$
The equation of the perpendicular line is
$\Rightarrow y=\frac{1}{2}x-3$.
