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

$$\begin{aligned} y & = - 0.1954 x + 17.6633 \\x+5.1177y-90.3956&=0\end{aligned}$$

After substituting: $ A = 1 $ , $ B = 5.1177 $ , $ C = -90.3956 $ , $ x_0 = 7.78 $ and $ y_0 = 15.63 $ we have:

$$ \begin{aligned} d =& \frac{ \left| 1\cdot7.78 +5.1177\cdot15.63 + \left( -90.3956\right) \right| }{\sqrt{ 1^2 + 5.1177^2}} = \\ d =& \frac{ \left| 7.78 + 79.9898 -90.3956 \right| }{\sqrt{ 1 + 26.1909}} = \\ d =& \frac{ \left| -2.6258 \right| }{\sqrt{ 27.1909}} = \\ d =& \frac{ 2.6258 }{ 5.2145 } = \\ d =& 0.5036 \end{aligned} $$

Line-point distance calculator