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

$$\begin{aligned} y & = - \frac{ 5 }{ 2 } x + 2 \\2 \cdot y &= 2 \cdot \left( - \frac{ 5 }{ 2 } x + 2 \right) \\2 \cdot y &= - 5 x + 4 \\5x+2y-4&=0\end{aligned}$$

After substituting: $ A = 5 $ , $ B = 2 $ , $ C = -4 $ , $ x_0 = 15 $ and $ y_0 = -21 $ we have:

$$ \begin{aligned} d =& \frac{ \left| 5\cdot15 +2\cdot\left(-21\right) + \left( -4\right) \right| }{\sqrt{ 5^2 + 2^2}} = \\ d =& \frac{ \left| 75 -42 -4 \right| }{\sqrt{ 25 + 4}} = \\ d =& \frac{ \left| 29 \right| }{\sqrt{ 29}} = \\ d =& \frac{ 29 }{ \sqrt{ 29 } } = \\ d =& \sqrt{ 29 } \end{aligned} $$

Line-point distance calculator