Question

The equation of a straight line passing through $(3,-1)$ and having intercepts equal in magnitude but opposite in sign is

• A. $x+y-2=0$
• B. $x-y-4=0$
• C. $x+3y=1$
• D. $x+2y-1=0$

Answer 1

The correct option is B $x-y-4=0$

The equation of straight line in intercept form is

$\Rightarrow$ $\frac{x}{a}+\frac{y}{b}=1$ ----- ( 1 )

$\Rightarrow$ $b=-1$ [ Given ]

So, equation ( 1 ) becomes,

$\Rightarrow$ $\frac{x}{a}+\frac{y}{(-a)}=1$

$\Rightarrow$ $\frac{x}{a}-\frac{y}{a}=1$

$\Rightarrow$ $\frac{x-y}{a}=1$

$\Rightarrow$ $x-y=a$ ----- ( 2 )

But this line passes through $(3,-1)$

$\Rightarrow$ $3+1=a$

$\therefore$ $a=4$

Substituting value of $a$ in ( 2 )

$\Rightarrow$ $x-y=4$

$\Rightarrow$ $x-y-4=0$