The equation of the line passing through point $ \left(-1,~9\right) $, and point $ \left(-4,~-4\right) $ is:
$$ 13x-3y+40=0 $$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:
$$ \begin{aligned} & \left(-1,~9\right) \implies x_A = -1 ~~\text{and}~~ y_A = 9 \\[1 em] & \left(-4,~-4\right) \implies x_B = -4 ~~\text{and}~~ y_B = -4 \end{aligned} $$After substituting into the formula, we obtain:
$$ \begin{aligned} y - y_A~&=~\frac{y_B - y_A}{x_B - x_A}(x - x_A) \\[1 em] y - 9~&=~\frac{ -4 - 9 }{ -4 - \left(-1\right) } \left( x - \left(-1\right) \right) \\[1 em]y - 9 ~&=~ \frac{ 13 }{ 3 } \left( x + 1 \right) \\[1 em]y - 9 ~&=~ \frac{ 13 }{ 3 }x + \frac{ 13 }{ 3 } \\[1 em]y ~&=~ \frac{ 13 }{ 3 }x + \frac{ 40 }{ 3 } \end{aligned} $$