Question

derive the equation of a line having X and Y intercept value as 'a' and 'b' respectively and hence find the equation of the line having X and Y intercept values as 2 and 6 respectively



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Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

TO DETERMINE

1. Derive the equation of a line having X and Y intercept value as 'a' and 'b' respectively

2. Hence find the equation of the line having X and Y intercept values as 2 and 6 respectively

CALCULATION

ANSWER TO QUESTION : 1

Let us take a general equation of any line as

$\sf{ lx + my = n\: } \: \: \: \: .....(1)$

Since the equation has X and Y intercept value as 'a' and 'b' respectively

So the line passes through the point A( a, 0)

and B( 0 , b )

Since the equation (1) passes through the point A( a, 0)

So

$\displaystyle \sf{ \: }la = n$

$\implies \displaystyle \sf{ \: }l = \frac{n}{a}$

Again the equation (1) passes through the point B( 0 , b )

$\displaystyle \sf{ \: } {mb} = n$

$\implies \displaystyle \sf{ \: }m = \frac{n}{b}$

Replacing the value of l and m in Equation (1)

$\displaystyle \sf{ \: } \frac{nx}{a} + \frac{ny}{b} = n$

$\implies \: \displaystyle \sf{ \: } \frac{x}{a} + \frac{y}{b} = 1 \: \: \: \: ....(2)$

Which is the required equation

Hence the equation of a line having X and Y intercept value as 'a' and 'b' respectively is

$\boxed{ \: \: \: \displaystyle \sf{ \: } \frac{x}{a} + \frac{y}{b} = 1 \: \: \: \: }$

ANSWER TO QUESTION : 2

Now the equation of the line having X and Y intercept values as 2 and 6 respectively

So a = 2 and b = 6

So From Equation (2) we get

$\displaystyle \sf{ \: } \frac{x}{2} + \frac{y}{6} = 1 \: \: \:$

Hence the required equation of the line is

$\boxed{\displaystyle \sf{ \: } \: \: \frac{x}{2} + \frac{y}{6} = 1 \: \: \: }$

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Answer 2

Answer:

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