The equation of the line passing through point $ \left(-4,~5\right) $, and point $ \left(-2,~-3\right) $ is:
$$ y = - 4 x - 11 $$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:
$$ \begin{aligned} & \left(-4,~5\right) \implies x_A = -4 ~~\text{and}~~ y_A = 5 \\[1 em] & \left(-2,~-3\right) \implies x_B = -2 ~~\text{and}~~ y_B = -3 \end{aligned} $$After substituting into the formula, we obtain:
$$ \begin{aligned} y - y_A~&=~\frac{y_B - y_A}{x_B - x_A}(x - x_A) \\[1 em] y - 5~&=~\frac{ -3 - 5 }{ -2 - \left(-4\right) } \left( x - \left(-4\right) \right) \\[1 em]y - 5 ~&=~ -4 \left( x + 4 \right) \\[1 em]y - 5 ~&=~ -4x-16 \\[1 em]y ~&=~ -4x-11 \end{aligned} $$