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

The equation of a line in the intercept form is $\frac{x}{a}+\frac{y}{b}=1$ ..(i)
where $a$ and $b$ are the intercepts on $x$ and $y$ axis respectively.
It is given that the line cuts off equal intercepts on both the axes. This means that $a=b$.
Accordingly, equation(i) reduces to,
$\frac{x}{a}+\frac{y}{b}=1$ $\Rightarrow x+y=a$ ...(ii)
Since the given line passes through point $(2,3)$, equation(ii) reduces to $2+3=a\Rightarrow a=5$
On substituting the value of a in equation (ii), we obtain
$x+y=5$ which is the required equation of the line.