Answer
\begin{array}{l}\require{cancel}
\\\text{Slope-Intercept Form: }
y=-\dfrac{3}{5}x-2
\\\text{Slope: }
-\dfrac{3}{5}
\end{array}
Work Step by Step
Using the properties of equality, in the form $y=mx+b$ (or the Slope-Intercept Form of Linear Equations), the given equation is equivalent to:
\begin{align*}
\dfrac{5y}{5}&=\dfrac{-3x-10}{5}
\\\\
y&=\dfrac{-3}{5}x-\dfrac{10}{5}
\\\\
y&=-\dfrac{3}{5}x-2
\end{align*}
Using $y=mx+b$ (where $m$ is the slope) then the given equation has the following properties
\begin{array}{l}\require{cancel}
\\\text{Slope-Intercept Form: }
y=-\dfrac{3}{5}x-2
\\\text{Slope: }
-\dfrac{3}{5}
\end{array}
