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Question
Find the equation of a straight line passing through (1, – 4) and has intercepts which are in the ratio 2 : 5
Solution
Let the x-intercept be 2a and the y-intercept 5a
The equation of a line is
`x/"a" + y/"a"` = 1
⇒ `x/(2"a") + y/(5"a")` = 1
The line passes through the point (1, – 4)
`1/(2"a")+ (-4)/(5"a")` = 1
⇒ `1/(2"a") - 4/(5"a")` = 1
Multiply by 10a
L.C.M. of 2a and 5a is 10a
5 – 8 = 10a
⇒ – 3 = 10a
a = `(-3)/(10)`
The equation of the line is
`x/(2((-3)/10)) + y/(5((-3)/10))` = 1
`x/((-3)/5) + y/((-3)/2)` = 1
⇒ `(5x)/(-3) + (2y)/(-3)` = 1
`(-5x)/3 - (2y)/3` = 1
Multiply by 3
– 5x – 2y = 3
⇒ – 5x – 2y – 3 = 0
5x + 2y + 3 = 0
The equation of a line is 5x + 2y + 3 = 0
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