Q. 145.0( 1 Vote )

# Find the equation

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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