Answer
$\frac{2}{\sqrt 41}$
Work Step by Step
We are given: $4x+5y=1$
Rewrite as: $y=\frac{1}{5}-\frac{4}{5}x$
From exercise 21, we have:
$d(P,L)=\frac{|y_0-x_0m-b|}{\sqrt 1+m^2}$
Since $P(1,-1)$ and $y=\frac{1}{5}-\frac{4}{5}x$, hence:
$$d(P,L)=\frac{|-1-1.(-\frac{4}{5})-\frac{1}{5}|}{\sqrt 1+(-\frac{4}{5})^2}=\frac{|-\frac{2}{5}|}{\sqrt \frac{41}{25}}=\frac{\frac{2}{5}}{\frac{\sqrt 41}{5}}=\frac{2}{\sqrt 41}$$
