Answer
$\color{blue}{y=-2x}$
Work Step by Step
RECALL:
(1) The slope-intercept form of a line's equation is:
$y=mx+b$
where $m$ = slope and $b$ = y-intercept
(2) Perpendicular lines have slopes whose product is $-1$ (negative reciprocals of each other).
The line we are looking for is perpendicular to $y=\frac{1}{2}x+4$ (whose slope is $\frac{1}{2}$).
This means that line has a slope of $-2$ (since $-2(\frac{1}{2})=-1$).
Thus, a tentative equation of the line we are looking for is:
$y=-2x+b$
To find the value of $b$, substitute the x and y values of the given point to obtain:
$y=-2x+b
\\-2 = -2(1)=b
\\-2 = -2 + b
\\-2+2=b
\\0=b$
Thus, the equation of the line is:
$y=-2x+0
\\\color{blue}{y=-2x}$
