#### Answer

(a) Standard form
$y=-4$
(b) Slope-intercept form
$y=-4$

#### Work Step by Step

RECALL:
(1) The standard form of a line's equation is $Ax+By=C$.
(2) The slope-intercept form of a line's equation is $y=mx+b$ where $m$=slope and $(0, b)$ is the line's y-intercept.
(3) Vertical lines and horizontal lines are perpendicular to each other.
(4) Horizontal lines have points that share the same y-coordinate.
The line is perpendicular to the vertical line $x=-2$. This means the line we are looking for is a horizontal line.
Since the the horizontal line contains the point $(4, -4)$, and a horizontal line's points share the same y-coordinate, then the equation of the line must we are looking for is $y=-4$.
(a) Standard form
$y=-4$
(b) Slope-intercept form
$y=-4$