# Find the equation of the line passing through the point (2, 2) and cutting off intercepts on the axes, whose sum is 9.

To Find: The equation of the line passing through the point (2, 2) and cutting off intercepts on the axes, whose sum is 9.

Given : Let a and b be two intercepts of x-axis and y-axis respectively.

sum of the intercepts is 9,i.e,a+b = 9

a = 9 – b or b = 9 – a

Formula used:

The equation of a line is given by:

= 1

The given point (2, 2) passing through the line and satisfies the equation of the line.

= 1

2(9 – a) + 2a = 9a – a2

18 – 2a +2a = 9a – a2

a2 – 9a + 18 = 0

a2 – 6a – 3a + 18 =0

a(a - 6) - 3(a - 6) = 0

(a - 3) (a - 6) = 0

a = 3, a = 6

when a = 3, b=6 and a=6, b=3

case 1 : when a=3 and b=6

Equation of the line : = 1

Hence, 2x + y = 6 is the required equation of the line.

case 2 : when a=6 and b=3

Equation of the line : = 1

= 1

Hence , x + 2y = 6 is the required equation of the line.

Therefore, 2x + y = 6 is the required equation of the line when a=3 and b=6.And , x + 2y = 6 is the required equation of the line when a=6 and b=3.

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