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