The equation of the line passing through point $ \left(5,~-4\right) $, and point $ \left(7,~3\right) $ is:
$$ y = \frac{ 7 }{ 2 } x - \frac{ 43 }{ 2 } $$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:
$$ \begin{aligned} & \left(5,~-4\right) \implies x_A = 5 ~~\text{and}~~ y_A = -4 \\[1 em] & \left(7,~3\right) \implies x_B = 7 ~~\text{and}~~ y_B = 3 \end{aligned} $$After substituting into the formula, we obtain:
$$ \begin{aligned} y - y_A~&=~\frac{y_B - y_A}{x_B - x_A}(x - x_A) \\[1 em] y - \left(-4\right)~&=~\frac{ 3 - \left(-4\right) }{ 7 - 5 } \left( x - 5 \right) \\[1 em]y + 4 ~&=~ \frac{ 7 }{ 2 } \left( x - 5 \right) \\[1 em]y + 4 ~&=~ \frac{ 7 }{ 2 }x-\frac{ 35 }{ 2 } \\[1 em]y ~&=~ \frac{ 7 }{ 2 }x-\frac{ 43 }{ 2 } \end{aligned} $$