Question

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

$\therefore -5+3=a$

$\Rightarrow a=-5+3=-2$

Required equation of the line is $x+y+2=0$