Question

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

• A. $x-y-8=0$
• B. $x+y-8=0$
• C. $x-y+8=0$
• D. None of these

Answer 1

Answer: (A)

$x-y-8=0$

Equation of a line whose,

$x-intercept=a$ and $y-intercept=b$ is

$\frac{x}{a}+\frac{y}{b}=1$

Here,

$x-intercept\left(a\right)=n$

$y-intercept\left(b\right)=-n$

$\frac{x}{n}+\frac{y}{(-n)}=1$ which is passing

Through the point $(5,-3)$ [ Given ]

$\frac{5}{n}+\frac{(-3)}{(-n)}=1$

$\frac{5}{n}+\frac{3}{n}=1$

$\frac{8}{n}=1$

$n=8$

Therefore,

$x-intercept\left(a\right)=n=8$

$y-intercept\left(b\right)=-n=-8$

Required equation,

$\frac{x}{8}-\frac{y}{8}=1$

$x-y=8$

$x-y-8=0$

Hence, this is the answer.