Answer
$y=2x+8$, or, in general form, $2x-y+8=0$
Work Step by Step
Through $(-3,2);$ perpendicular to the line $y=-\frac{1}{2}x+7$
Use the point-slope form of the equation of a line, which is $y-y_{1}=m(x-x_{1})$, where $(x_{1},y_{1})$ is a point through which the line passes and $m$ is the slope.
$(x_{1},y_{1})$ and a line perpendicular to the one we have to find are given.
The equation given is in slope-intercept form, so it's evident that its slope is $-\frac{1}{2}$.
Since the slopes of perpendicular lines are negative reciprocals, the slope of the line we have to find is:
$m=-\dfrac{1}{\Big(-\dfrac{1}{2}\Big)}=2$
Now that $(x_{1},y_{1})$ and $m$ are known, substitute them into the point-slope form of the equation of a line formula and simplify to obtain the equation of the line we have to find:
$y-y_{1}=m(x-x_{1})$
$y-2=2(x+3)$
$y-2=2x+6$
$y=2x+6+2$
$y=2x+8$, or, in general form, $2x-y+8=0$