Find the equation of the straight lines passing through the point (2, 2) and the sum of the intercepts is 9.

Let the x intercept be ‘a’ and the y intercept be ‘b’ . it is given that

a + b = 9

The equation of the line using the intercept form is

Substituting b = 9– a in this equation

⇒

⇒ x (9–a) + ya = a(9 –a)

The point (2, 2) lies on this line and thus it satisfies the equation

x (9–a) + ya = a(9 –a)

⇒ 2(9 –a) + 2a = a ( 9–a)

⇒ 18 –2a + 2a = 9a –a²

⇒ a² – 9a + 18 = 0

⇒ a² – 3a –6a + 18 = 0

⇒ a ( a– 3) –6 (a –3) = 0

⇒ (a–6) (a–3) = 0

⇒ a = 6 or 3

The equation of the line is

x( 9–3) + y(3) = 3(9–3)

⇒ 6x + 3y = 18

⇒ 2x + y –6 = 0

Or

x(9–6) + y(6) = 6(9–6)

3x + 6y = 18

⇒ x + 2y –6 = 0