The equation of the line passing through point $ \left(3,~2\right) $, and point $ \left(9,~7\right) $ is:
$$ 5x-6y-3=0 $$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:
$$ \begin{aligned} & \left(3,~2\right) \implies x_A = 3 ~~\text{and}~~ y_A = 2 \\[1 em] & \left(9,~7\right) \implies x_B = 9 ~~\text{and}~~ y_B = 7 \end{aligned} $$After substituting into the formula, we obtain:
$$ \begin{aligned} y - y_A~&=~\frac{y_B - y_A}{x_B - x_A}(x - x_A) \\[1 em] y - 2~&=~\frac{ 7 - 2 }{ 9 - 3 } \left( x - 3 \right) \\[1 em]y - 2 ~&=~ \frac{ 5 }{ 6 } \left( x - 3 \right) \\[1 em]y - 2 ~&=~ \frac{ 5 }{ 6 }x-\frac{ 5 }{ 2 } \\[1 em]y ~&=~ \frac{ 5 }{ 6 }x-\frac{ 1 }{ 2 } \end{aligned} $$