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 formed by Two intercepts is $\frac{x}{a}+\frac{y}{b}=1$

Given that, $a=b$

Since the line is passing through the point $(2,3)$

So, $\frac{2}{a}+\frac{3}{a}=1$

$⟹\frac{5}{a}=1$

$\therefore a=5$

Hence, $b=5$

The equation of the line is $\frac{x}{5}+\frac{y}{5}=1$ (or) $x+y-5=0$