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

Concept Used:

The equation of the line with intercepts a and b is

Given:

Here, a+b = 9

Explanation:

b = 9 – a ……(i)

The line is passing through (2, 2).

……(ii)

From equation (i) and (ii)

18 – 2a + 2a = 9a – a2

a2 – 9a +18 = 0

(a – 3)(a – 6) = 0

a = 3, 6

For a = 3, b = 9 – 3 = 6

For a = 6, b = 9 – 6 = 3

Thus the equation of line is

or

2x + y = 6 or x + 2y = 6

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

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