Find the equation of the straight line
Question:

Find the equation of the straight line which passes through the point (1, – 2) and cuts off equal intercepts from axes.

Solution:

The equation of line in intercept form is

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

Where $a$ and $b$ are the intercepts on the axis. Given that $a=b$

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

The above equation can be written as

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

On cross multiplication we get

$\Rightarrow x+y=a \ldots .1$

If equation 1 passes through the point $(1,-2)$, we get

$x=1$ and $y=-2$

$1+(-2)=a$

$\Rightarrow 1-2=\mathrm{a}$

$\Rightarrow a=-1$

Putting the value of a in equation 1 , we get

$x+y=-1$

$\Rightarrow x+y+1=0$

Hence, the equation of straight line is $x+y+1=0$ which passes through the point $(1,-2)$.