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

$$\begin{aligned} y & = - 5 x - 9 \\5x+y+9&=0\end{aligned}$$

After substituting: $ A = 5 $ , $ B = 1 $ , $ C = 9 $ , $ x_0 = 1 $ and $ y_0 = -4 $ we have:

$$ \begin{aligned} d =& \frac{ \left| 5\cdot1 +1\cdot\left(-4\right) + 9 \right| }{\sqrt{ 5^2 + 1^2}} = \\ d =& \frac{ \left| 5 -4 + 9 \right| }{\sqrt{ 25 + 1}} = \\ d =& \frac{ \left| 10 \right| }{\sqrt{ 26}} = \\ d =& \frac{ 10 }{ \sqrt{ 26 } } = \\ d =& \frac{ 5 \sqrt{ 26}}{ 13 } \end{aligned} $$

Line-point distance calculator