#### Answer

$m=\dfrac{2}{3}$

#### Work Step by Step

Using the properties of equality, the given equation, $
3y=2x+5
$ is equivalent to
\begin{array}{l}\require{cancel}
y=\dfrac{2}{3}x+\dfrac{5}{3}
.\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{2}{3}
.\end{array}
Since parallel lines have the same slope, then a line parallel to the equation above will also have $
m=\dfrac{2}{3}
.$