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

(x₁ , y₁) = A(a,0)

(x₂ , y₂) = B(0, b)

Where a and b are intercepts of the line.

Formula used:

The equation of the line is : = 1

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

(x ,y) =

= =

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

= 5 a = 20 , = 6 b= 8

Equation of the line becomes = 1

8x +20y = 160

2x +5y = 40

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