Answer
$y=\frac{2}{3}x-\frac{23}{3}$.
Work Step by Step
Want: Parallel to $y=\frac{2}{3}x+5$ and contains the point$\left( -2,-9 \right)$.
The line $y=\frac{2}{3}x+5$ has slope $\frac{2}{3}$. As the required line is parallel to the line $y=\frac{2}{3}x+5$, the required line has slope $\frac{2}{3}$.
Put the values of slope and the point $\left( -2,-9 \right)$ in the point slope form of a straight line.
$\begin{align}
& \left( y-{{y}_{1}} \right)=m\left( x-{{x}_{1}} \right) \\
& y+9=\frac{2}{3}\left( x+2 \right)
\end{align}$
Simplify further.
$\begin{align}
& y+9=\frac{2}{3}x+\frac{4}{3} \\
& y=\frac{2}{3}x-\frac{23}{3}
\end{align}$
