The equation of the line passing through point $ \left(9,~-6\right) $, and point $ \left(-3,~-4\right) $ is:
$$ x+6y+27=0 $$To find equation of the line passing through points $ A(x_A,y_A) $ and $ B(x_B,y_B) $, we use formula:
$$ y - y_A~=~\frac{y_B - y_A}{x_B - x_A}(x-x_A) $$In this example we have:
$$ \begin{aligned} & \left(9,~-6\right) \implies x_A = 9 ~~\text{and}~~ y_A = -6 \\[1 em] & \left(-3,~-4\right) \implies x_B = -3 ~~\text{and}~~ y_B = -4 \end{aligned} $$After substituting into the formula, we obtain:
$$ \begin{aligned} y - y_A~&=~\frac{y_B - y_A}{x_B - x_A}(x - x_A) \\[1 em] y - \left(-6\right)~&=~\frac{ -4 - \left(-6\right) }{ -3 - 9 } \left( x - 9 \right) \\[1 em]y + 6 ~&=~ -\frac{ 1 }{ 6 } \left( x - 9 \right) \\[1 em]y + 6 ~&=~ -\frac{ 1 }{ 6 }x + \frac{ 3 }{ 2 } \\[1 em]y ~&=~ -\frac{ 1 }{ 6 }x-\frac{ 9 }{ 2 } \end{aligned} $$