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

Question:

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

Solution:

The equation of a line in the intercept form is

$\frac{x}{a}+\frac{y}{b}=1$ $\ldots$ (i)

Here, a and b are the intercepts on x and y axes 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

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

$\Rightarrow x+y=a$ $\ldots$ (ii)

Since the given line passes through point (2, 3), equation (ii) reduces to

2 + 3 = a ⇒ a = 5

On substituting the value of a in equation (ii), we obtain

x + y = 5, which is the required equation of the line