The equation of the line passing through point $ \left(-3,~-4\right) $, and point $ \left(7,~4\right) $ is:
$$ 4x-5y-8=0 $$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:
$$ \begin{aligned} & \left(-3,~-4\right) \implies x_A = -3 ~~\text{and}~~ y_A = -4 \\[1 em] & \left(7,~4\right) \implies x_B = 7 ~~\text{and}~~ y_B = 4 \end{aligned} $$After substituting into the formula, we obtain:
$$ \begin{aligned} y - y_A~&=~\frac{y_B - y_A}{x_B - x_A}(x - x_A) \\[1 em] y - \left(-4\right)~&=~\frac{ 4 - \left(-4\right) }{ 7 - \left(-3\right) } \left( x - \left(-3\right) \right) \\[1 em]y + 4 ~&=~ \frac{ 4 }{ 5 } \left( x + 3 \right) \\[1 em]y + 4 ~&=~ \frac{ 4 }{ 5 }x + \frac{ 12 }{ 5 } \\[1 em]y ~&=~ \frac{ 4 }{ 5 }x-\frac{ 8 }{ 5 } \end{aligned} $$