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

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

To apply this formula, we first need to express the line in standard form

$$\begin{aligned} y & = - \frac{ 3 }{ 4 } x - 2 \\4 \cdot y &= 4 \cdot \left( - \frac{ 3 }{ 4 } x - 2 \right) \\4 \cdot y &= - 3 x - 8 \\3x+4y+8&=0\end{aligned}$$

After substituting: $ A = 3 $ , $ B = 4 $ , $ C = 8 $ , $ x_0 = 3 $ and $ y_0 = -43 $ we have:

$$ \begin{aligned} d =& \frac{ \left| 3\cdot3 +4\cdot\left(-43\right) + 8 \right| }{\sqrt{ 3^2 + 4^2}} = \\ d =& \frac{ \left| 9 -172 + 8 \right| }{\sqrt{ 9 + 16}} = \\ d =& \frac{ \left| -155 \right| }{\sqrt{ 25}} = \\ d =& \frac{ 155 }{ 5 } = \\ d =& 31 \end{aligned} $$

Line-point distance calculator