The equation of the line passing through point $ \left(3,~4\right) $, and point $ \left(3,~8\right) $ is:
$$ x-3=0 $$In this example we have:
$$ \begin{aligned} & \left(3,~4\right) \implies \color{blue}{x_A = 3} ~~\text{and}~~ y_A = 4 \\[1 em] & \left(3,~8\right) \implies \color{blue}{x_B = 3} ~~\text{and}~~ y_B = 8 \end{aligned} $$Since, $ x_A = x_B $ the equation of the line is:
$$ x = x_A $$In this example this is:
$$ x = 3 $$