Answer
\begin{array}{l}\require{cancel}
\\\text{Slope: }
-\dfrac{1}{2}
\\\text{$y$-intercept: }
\left(0, -\dfrac{5}{2}\right)
\end{array}
Work Step by Step
Using the properties of equality, in the form $y=mx+b,$ the given equation is equivalent to
\begin{array}{l}\require{cancel}
-3\left( -\dfrac{1}{3}x-\dfrac{2}{3}y \right)=\left( \dfrac{5}{3} \right)(-3)
\\\\
-1(-x)-1(-2y)=(5)(-1)
\\
x+2y=-5
\\
2y=-x-5
\\\\
\dfrac{2y}{2}=\dfrac{-x-5}{2}
\\\\
y=-\dfrac{1}{2}x-\dfrac{5}{2}
.\end{array}
Using $y=mx+b$ (where $m$ is the slope and $(0, b)$ is the $y$-intercept) or the Slope-Intercept Form of linear equations, then the equation above has the following properties
\begin{array}{l}\require{cancel}
\\\text{Slope: }
-\dfrac{1}{2}
\\\text{$y$-intercept: }
\left(0, -\dfrac{5}{2}\right)
.\end{array}
