#### Answer

$m=-\dfrac{4}{7}$

#### Work Step by Step

Using the properties of equality, the given equation, $
4x+7y=3
$ is equivalent to
\begin{array}{l}\require{cancel}
7y=-4x+3
\\\\
y=-\dfrac{4}{7}x+\dfrac{3}{7}
.\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=-\dfrac{4}{7}
.\end{array}