Answer
The equation of the perpendicular line is
$y=-2x+24$.
Work Step by Step
The given point is $(7,10)$.
The given equation of the line is
$\Rightarrow y=\frac{1}{2}x-9$
Slope of the line is $m=\frac{1}{2}$.
Slope of the perpendicular line is $m=-2$.
The slope-intercept form is
$\Rightarrow y=mx+b$
Substitute $-2$ for $m,7$ for $x,$ and $10$ for $y$.
$\Rightarrow 10=-2(7)+b$
Simplify.
$\Rightarrow 10=-14+b$
Add $14$ to each side.
$\Rightarrow 10+14=-14+b+14$
Simplify.
$\Rightarrow 24=b$.
The equation of the perpendicular line is
$\Rightarrow y=-2x+24$.
