Let the intercepts made by the line on the x-axis and y-axis be a and 9 – a respectively. Then its equation is

x

a

+

y

9−a

= 1
Since it passes through point (2, 2), we have

2

a

+

2

9−a

= 1
⇒ 2(9 – a) + 2a = a(9 – a) ⇒ 18 – 2a + 2a = 9a – a2
⇒ 18 = 9a – a2 ⇒ a2 – 9a + 18 = 0 ⇒ a2 – 6a – 3a + 18 = 0
⇒ a(a – 6) – 3 (a – 6) = 0 ⇒ a = 3, 6
Now, if a = 3 ⇒ b = 9 – 3 = 6 and if a = 6 ⇒ b = 9 – 6 = 3
So, required equation is

x

3

+

y

6

= 1 or

x

6

+

y

3

= 1
i.e., 2x + y – 6 = 0 or x + 2y – 6 = 0.