Find equati

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.