Question

Find the equation of the line passing through the point (1, 5) and also divides the co-ordinate axes in the ratio 3:10

Answer 1

Let the line divide the coordinate axis in the ratio 3 : 10.

∴ x-intercept = 3k

y-intercept = 10k

∴ The equation of the straight line is `x/(3"k") + y/(10"k")` = 1

This line passes through the point P(1, 5).

∴ `1/(3"k") + 5/(10"k")` = 1

`1/(3"k") + 1/(2"k")` = 1

`(2"k"+ 3 "k")/(2"k" xx 3"k")` = 1

`(5"k")/(2"k" xx 3"k")` = 1

`5/(6"k")` = 1

⇒ k = `5/6`

∴ The required equation is

`x/(3(5/6)) + y/(10(5/6))` = 1

`x/(5/2) + y/(25/3)` = 1

`(2x)/5 + (3y)/25` = 1

`(10x + 3y)/25` = 1

10x + 3y = 25