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

Let the equation of the line be $$ \frac{x}{a}+\frac{y}{b}=1 $$ The line meets the coordinate axes at $A(a, 0)$ and $B(0, b)$ respectively. The coordinate of the point which divides the line joining $A(a, 0)$ and $B(0, b)$ in the ratio $3: 2$ are $$ \left(\frac{3 \times 0+2 \times a}{3+2}, \frac{3 \times b+2 \times 0}{3+2}\right) \Rightarrow\left(\frac{2 a}{5}, \frac{3 b}{5}\right) $$ If is given that, the point $(2,-1)$ divides the $A B$ in the ratio $3: 2$. $$ \therefore \frac{2 a}{5}=2 \text { and } \frac{3 b}{5}=-1 \Rightarrow a=5 \text { and } b=\frac{-5}{3} $$ Hence, the required equation of the required line is $$ \begin{array}{rlrl} & & \frac{x}{5}+\frac{y}{\frac{-5}{3}} & =1 \\ \Rightarrow & \frac{x}{5}-\frac{3 y}{5} & =1 \\ \Rightarrow & x-3 y & =5 \\ \Rightarrow & x-3 y-5 & =0 \end{array} $$