Question

Find the equation of line passing through $(2,5)$ and making intercepts equal in the magnitude but opposite in sign on both the axes.

Answer 1

Let $x$-intercept of the line be $a$.
Then, $y$-intercept of the line is $-a$.
$\therefore$ Equation of the line using double intercept form is $\frac{x}{a}+\frac{y}{(-a)}=1$
$\frac{x}{a}-\frac{y}{a}=1$
i.e. $x-y=a$ ...(1)
This line passes through the point $(2,5)$
$\therefore 2-5=a$
i.e. $a=-3$
From (1), equation of the line is $x-y=-3$
i.e., $x-y+3=0$.