The distance from the point $ (x_0, y_0) $ to the line $ Ax + By + C = 0 $ is given by:

$$ d = \frac{ \left| Ax_0 + B_yo + C \right| }{ \sqrt{A^2 + B^2}} $$

After substituting: $ A = 4 $ , $ B = 3 $ , $ C = 7 $ , $ x_0 = 3 $ and $ y_0 = 4 $ we have:

$$ \begin{aligned} d =& \frac{ \left| 4\cdot3 +3\cdot4 + 7 \right| }{\sqrt{ 4^2 + 3^2}} = \\ d =& \frac{ \left| 12 + 12 + 7 \right| }{\sqrt{ 16 + 9}} = \\ d =& \frac{ \left| 31 \right| }{\sqrt{ 25}} = \\ d =& \frac{ 31 }{ 5 } = \\ d =& \frac{ 31 }{ 5 } \end{aligned} $$

Line-point distance calculator