Answer
$y=2x+8$
Work Step by Step
RECALL:
(1) Perpendicular lines have slopes whose product is $-1$ (or negative reciprocal slopes).
(2) The slope-intercept form of a line's equation is $y=mx+b$, where $m$ = slope and $b$ = y-intercept.
The line is perpendicular to the line $y=-\dfrac{1}{2}x+7$ whose slope is $-\dfrac{1}{2}$.
This means that slope of the line we are looking for is $2$ (the negative reciprocal of $-\frac{1}{2}$).
Thus, the tentative equation of the line is:
$y=2x+b$
The line passes through the point $(-3, 2)$.
To find the value of $b$, substitute the x and y coordinates of this point into the tentative equation above to obtain:
$y=2x+b
\\2=2(-3) + b
\\2 = -6 + b
\\2+6 = b
\\8=b$
Therefore, the equation of the line is $y=2x+8$.
