If the portion of a line intercepted between the coordinate axes is divided by the point (2, -1) in the ratio 3:2 then the equation of that line is

Let the line be $\frac{x}{a}+\frac{y}{b}=1$

Let A(a, 0) B(0, b)

P(2,-1) divides AB in the ratio 3: 2

$\begin{array}{l}\therefore P\left(2,-1\right)=\left(\frac{3\left(0\right)+2\left(a\right)}{3+2},\frac{3\left(b\right)+2\left(0\right)}{3+2}\right)\\ \left(2,-1\right)=\left(\frac{2a}{5},\frac{3b}{5}\right)\end{array}$

$\begin{array}{l}\frac{2a}{5}=2\text{\hspace{0.17em} , }\frac{3b}{5}=-1\\ a=5 , b=\frac{-5}{3}\end{array}$

from (i) 

$\begin{array}{l} \frac{x}{5}+\frac{y}{\left(\frac{-5}{3}\right)}=1\\ \Rightarrow \frac{x}{5}-\frac{3y}{5}=1\\ \Rightarrow x-3y=5\end{array}$