The equation of the line passing through point $ \left(-4,~6\right) $, and point $ \left(-1,~0\right) $ is:
$$ y = - 2 x - 2 $$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:
$$ \begin{aligned} & \left(-4,~6\right) \implies x_A = -4 ~~\text{and}~~ y_A = 6 \\[1 em] & \left(-1,~0\right) \implies x_B = -1 ~~\text{and}~~ y_B = 0 \end{aligned} $$After substituting into the formula, we obtain:
$$ \begin{aligned} y - y_A~&=~\frac{y_B - y_A}{x_B - x_A}(x - x_A) \\[1 em] y - 6~&=~\frac{ 0 - 6 }{ -1 - \left(-4\right) } \left( x - \left(-4\right) \right) \\[1 em]y - 6 ~&=~ -2 \left( x + 4 \right) \\[1 em]y - 6 ~&=~ -2x-8 \\[1 em]y ~&=~ -2x-2 \end{aligned} $$