Answer
The function with slope $-2$ and passing through the point $\left( -4,\ 3 \right)$ is $y=-2x-5$.
Work Step by Step
The equation of the line is $y-{{y}_{1}}=m\left( x-{{x}_{1}} \right)$.
Here, the point $\left( {{x}_{1}},\ {{y}_{1}} \right)=\left( -4,\ 3 \right)$ and slope $m=-2$.
So, plugging in the values of $\left( {{x}_{1}},\ {{y}_{1}} \right)$ and m, we get
$\begin{align}
& y-{{y}_{1}}=m\left( x-{{x}_{1}} \right) \\
& y-3=\left( -2 \right)\left( x-\left( -4 \right) \right) \\
& y=-2x-8+3 \\
& =-2x-5
\end{align}$
