#### Answer

$x+4y=-12$

#### Work Step by Step

The slope-intercept form of a straight line is $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept.
Since the values of $m$ and $b$ are given in the question, we substitute these values into the equation:
$y=mx+b$
$y=-\frac{1}{4}x-3$
$y=\frac{-1x-3(4)}{4}$
$y=\frac{-1x-12}{4}$
$4y=-x-12$
$x+4y=-12$
Therefore, the equation of the line is $x+4y=-12$.