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 = 3 $ , $ B = 4 $ , $ C = 7 $ , $ x_0 = -2 $ and $ y_0 = -9 $ we have:

$$ \begin{aligned} d =& \frac{ \left| 3\cdot\left(-2\right) +4\cdot\left(-9\right) + 7 \right| }{\sqrt{ 3^2 + 4^2}} = \\ d =& \frac{ \left| -6 -36 + 7 \right| }{\sqrt{ 9 + 16}} = \\ d =& \frac{ \left| -35 \right| }{\sqrt{ 25}} = \\ d =& \frac{ 35 }{ 5 } = \\ d =& 7 \end{aligned} $$

Line-point distance calculator