#### Answer

$m=-\dfrac{1}{3}$

#### Work Step by Step

Using the properties of equality, the given equation, $
3x-y=4
$ is equivalent to
\begin{array}{l}\require{cancel}
-y=-3x+4
\\\\
y=3x-4
.\end{array}
Using $y=mx+b$ where $m$ is the slope, then the slope, $m$, of the equation above is
\begin{array}{l}\require{cancel}
m=3
.\end{array}
Since perpendicular lines have negative-reciprocal slopes, then a line perpendicular to the equation above will have $
m=-\dfrac{1}{3}
.$