Find the equation of the line which passes through the point
Question:

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

Solution:

To Find: The equation of the line passing through (3, -5) and cuts off intercepts on the axes which are equal in magnitude but opposite in sign.

Given : Let a and b be two intercepts of $x$-axis and $y$-axis respectively.

According to the question $a=-b$ or $b=-a$

And $(3,-5)$ passes through the point $(x, y)$, thus satisfies the equation

Formula used:

Now since intercept form of the line is given by ,

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

$\frac{3}{a}+\frac{-5}{-a}=1$

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

$a=8$ and $b=-8$

Equation of the line is $\frac{x}{8}+\frac{y}{-8}=1$

$\Rightarrow$ Hence, the required equation of the line is $\frac{x}{8}-\frac{y}{8}=1 \Rightarrow x-y=8$

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