Answer
$y=-3x-1$
Work Step by Step
The equation of the line passing through the point $(-2,5)$ is:
$$\begin{align*}
y-5&=m(x-(-2))\\
y-5&=m(x+2).
\end{align*}$$
In order to determine the slope $m$ we use the slope $m_1$ of the line $3x+y=9$. We determine the slope $m_1$:
$$\begin{align*}
3x+y&=9\\
y&=-3x+9.
\end{align*}$$
It means that $m_1=-3$.
Since our line is parallel to the line of slope $m_1=-3$, it means they have the same slope:
$$m=m_1=-3.$$
Now our line's equation is fully determined. We bring it to the slope-intercept:
$$\begin{align*}
y-5&=-3(x+2)\\
y&=-3x-6+5\\
y&=-3x-1.
\end{align*}$$
