Find equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.

We know that equation of the line making intercepts a and b on x-and y-axis, respectively, is . … (1)

Given, sum of intercepts = 9

∴ a + b = 9

⇒ b = 9 - a

Substituting b value in the above equation,

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

So,

⇒ 18 = a (9 – a)

⇒ 18 = 9a – a²

⇒ a² – 9a + 18 = 0

Factorizing,

⇒ a² – 3a – 6a + 18 = 0

⇒ a (a – 3) – 6 (a – 3) = 0

⇒ (a – 3) (a – 6) = 0

∴ a = 3 or a = 6

Substituting in (1),

Case 1 (a = 3):

Then b = 9 – 3 = 6

⇒

⇒ 2x + y = 6

⇒ 2x + y – 6 = 0

Case 2 (a = 6):

Then b = 9 – 6 = 3

⇒

⇒ x + 2y = 6

⇒ x + 2y – 6 = 0

Ans. The equation of the line is 2x + y – 6 = 0 or x + 2y – 6 = 0.