Answer
Point-slope form $y−3=2(x+2)$.
Slope-intercept form $y=2x+7$.
Work Step by Step
If the line passes through a point $(x_1,y_1)$ and slope is m then point-slope form of the perpendicular line is.
$\Rightarrow y−y_1=m(x−x_1)$
From the question we have
$\Rightarrow (x_1,y_1)=(−2,3)$
Equation of the perpendicular line.
$\Rightarrow y=-\frac{1}{2}x-4$
It is in the form of slope-intercept form $y=mx+c$.
The slope of the equation is $m=-\frac{1}{2}$
The slope of the two perpendicular lines are negative reciprocals to each other.
The slope of the required line is
$\Rightarrow m=\frac{1}{−\frac{1}{2}}$
$\Rightarrow m=2$
Substitute all values into the point-slope equation.
$\Rightarrow y−(3)=(2)(x−(−2))$
Simplify.
$\Rightarrow y−3=2(x+2)$
The above equation is the point-slope form.
Now isolate y
$\Rightarrow y−3=2(x+2)$
Use distributive property.
$\Rightarrow y−3=2x+4$
Add 3 to both sides.
$\Rightarrow y−3+3=2x+4+3$
Simplify.
$\Rightarrow y=2x+7$
The above equation is the slope-intercept form.
