Question

Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point $(2,3)$.

Answer 1

Equation of a line by intercept form is $\frac{x}{a}+\frac{y}{b}=1$

But given that $xandy$ intercept are equal

$\therefore a=b$

Thus, equation of line is
$\Rightarrow \frac{x}{a}+\frac{y}{a}=1(Asb=a)$

$\Rightarrow x+y=a$

$\Rightarrow x+y-a=0$

Now we need to find value of $a$

Given, the line passes through the point $(2,3)$

Point $(2,3)$ satisfies the equation of line

$\Rightarrow 2+3–a=0$

$\Rightarrow a=5$

Hence the required equation of line is

$x+y-5=0$