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

We know that equation of the line making intercepts a and b on x-and y-axis, respectively, is

Given that the line cuts off equal intercepts on the coordinate axes i.e. a = b.

So,

⇒ x + y = a … (1)

Given point = (2, 3)

∴ 2 + 3 = a

⇒ a = 5

Substituting a value in (1),

⇒ x + y = 5

⇒ x + y – 5 = 0

Ans. The equation of the line is x + y – 5 = 0.