# Find the equation of the line whose portion intercepted between the

Question:

Find the equation of the line whose portion intercepted between the coordinate axes is divided at the point (5, 6) in the ratio 3 : 1.

Solution:

To Find: The equation of the line whose portion intercepted between the coordinate axes is divided at the point (5, 6) in the ratio 3 : 1.

Given : The coordinate axes is divided in the ratio 3 : 1

$\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right)=\mathrm{A}(\mathrm{a}, 0)$

$\left(\mathrm{x}_{2}, \mathrm{y}_{2}\right)=\mathrm{B}(0, \mathrm{~b})$

Where a and b are intercepts of the line.

Formula used:

The equation of the line is :

The equation of the line is: $\frac{x}{a}+\frac{y}{b}=1$

And the co-ordinate axis is divided at (5,6) , thus by using Section formula

$(x, y)=\left(\frac{m y_{1}+n x_{1}}{m+n}, \frac{m y_{2}+n x_{2}}{m+n}\right)$

$=\left(\frac{3 * 0+a}{4}, \frac{3 b}{4}\right)=\left(\frac{a}{4}, \frac{3 b}{4}\right)$

(5,6) divides the co-ordinate axis, thus (x,y)= (5,6).

$\frac{a}{4}=5 \Rightarrow a=20, \frac{3 b}{4}=6 \Rightarrow b=8$

Equation of the line becomes $\frac{\mathrm{x}}{20}+\frac{\mathrm{y}}{8}=1$

$8 x+20 y=160$

$2 x+5 y=40$

Hence the required equation of the line is 2x +5y = 40.