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

$$\begin{aligned} y & = \frac{ 1 }{ 2 } x + 7 \\2 \cdot y &= 2 \cdot \left( \frac{ 1 }{ 2 } x + 7 \right) \\2 \cdot y &= x + 14 \\x-2y+14&=0\end{aligned}$$

After substituting: $ A = 1 $ , $ B = -2 $ , $ C = 14 $ , $ x_0 = -\frac{ 1 }{ 4 } $ and $ y_0 = 5 $ we have:

$$ \begin{aligned} d =& \frac{ \left| 1\cdot\left(-\frac{ 1 }{ 4 }\right) +\left(-2\right)\cdot5 + 14 \right| }{\sqrt{ 1^2 + (-2)^2}} = \\ d =& \frac{ \left| -\frac{ 1 }{ 4 } -10 + 14 \right| }{\sqrt{ 1 + 4}} = \\ d =& \frac{ \left| \frac{ 15 }{ 4 } \right| }{\sqrt{ 5}} = \\ d =& \frac{ \frac{ 15 }{ 4 } }{ \sqrt{ 5 } } = \\ d =& \frac{ 3 \sqrt{ 5}}{ 4 } \end{aligned} $$

Line-point distance calculator