Question

Find the equation of the line passing through $(5,-3)$ and whose intercepts on the axes are equal in magnitude but opposite in sign.

Answer 1

Let the intercepts be $a$ and $-a$

Equation of the line is $\frac{x}{a}+\frac{y}{b}=1$

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

$\Rightarrow x-y=a$

The line passes through $(5,-3)$

$\therefore 5-(-3)=a$

$\Rightarrow a=5+3=8$

Required equation of the line is $x-y-8=0$.