Answer :

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


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