Find the equation of the straight line which passes through the point

1.	Find the equation of the straight line which passes through the point (2, 3) and makes intercepts equal in magnitude but opposite in sign on the axes.
Answer» $\mathtt{\huge{\underline{\bf{\red{Given :-}}}}}$ The straight line which PASSES through the point (2, 3). It makes intercepts equal in MAGNITUDE but opposite in sign on the axes. $\mathtt{\huge{\underline{\bf{\green{To\:Find :-}}}}}$ The equation of the straight line. $\mathtt{\huge{\underline{\bf{\pink{Solution :-}}}}}$ ★ A line which can be extended from both sides without MAKING any curves till infinity is CALLED a straight line. General equation of straight line ax + by + c = 0 _____________________________________ Using, $\dfrac{x}{a} + \dfrac{y}{a} = 1$ According to the question, It makes intercepts equal in magnitude but opposite in sign on the axes. For Equation 1 :- $\dfrac{x}{-a} + \dfrac{y}{a} = 1$ ➝ $\dfrac{ y - x}{a} = 1$ ➝ y - x = a ➝ a = y - x .......(a) The straight line passes through the point (2, 3). ➝ a = 3 - 2 ➝ a = 1 .........(b) Comparing equation a & b , ➝ y - x = 1 ➝ - x + y = 1 For Equation 2 :- $\dfrac{x}{a} + \dfrac{y}{-a} = 1$ ➝ $\dfrac{ x - y }{a} = 1$ ➝ x - y = a ➝ a = x - y .......( k ) The straight line passes through the point (2, 3). ➝ a = 2 - 3 ➝ a = - 1 .........(l) Comparing equation k & l , ➝ x - y = 1 ➝ x - y = - 1 _______________________________________

Find the equation of the straight line which passes through the point (2, 3) and makes intercepts equal in magnitude but opposite in sign on the axes.

Answer»

$\mathtt{\huge{\underline{\bf{\red{Given :-}}}}}$

The straight line which PASSES through the point (2, 3).

It makes intercepts equal in MAGNITUDE but opposite in sign on the axes.

$\mathtt{\huge{\underline{\bf{\green{To\:Find :-}}}}}$

The equation of the straight line.

$\mathtt{\huge{\underline{\bf{\pink{Solution :-}}}}}$

★ A line which can be extended from both sides without MAKING any curves till infinity is CALLED a straight line.

General equation of straight line

ax + by + c = 0

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Using,

$\dfrac{x}{a} + \dfrac{y}{a} = 1$

According to the question,

It makes intercepts equal in magnitude but opposite in sign on the axes.

For Equation 1 :-

$\dfrac{x}{-a} + \dfrac{y}{a} = 1$

➝ $\dfrac{ y - x}{a} = 1$

➝ y - x = a

➝ a = y - x .......(a)

The straight line passes through the point (2, 3).

➝ a = 3 - 2

➝ a = 1 .........(b)

Comparing equation a & b ,

➝ y - x = 1

➝ - x + y = 1

For Equation 2 :-

$\dfrac{x}{a} + \dfrac{y}{-a} = 1$

➝ $\dfrac{ x - y }{a} = 1$

➝ x - y = a

➝ a = x - y .......( k )

The straight line passes through the point (2, 3).

➝ a = 2 - 3

➝ a = - 1 .........(l)

Comparing equation k & l ,

➝ x - y = 1

➝ x - y = - 1

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