Question

find the equation of the line passing to the point (2,2) and cutting of intercepts on the axis whose sum is 9

Answer 1

Write the intercept form of equation of a straight line-
y/a + x/b = 1
Where a + b = 9
Also satisfy the point and get the equation!

Answer 2

Answer:

2 x + y - 6 = 0

And

x + 2 y - 6 = 0.

Step-by-step explanation:

Given :

Sum of intercepts is 9.

i.e. a + b = 9

a = 9 - b

In order to find equation of line we have :

x / a + y / b = 1

x / a + y / ( 9 - b ) = 1

9 x - a x + a y = 9 a - a²

Given point ( 2 , 2 ) as it passing then it is solution of equation.

Putting x = 2 and y = 2

18 - 2 a + 2 a =  9 a - a²

a² - 9 a + 18 = 0

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

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

a = 3 or a = 6

We have :

a + b = 9

When a = 3

b = 6

Also when a = 6

b = 3.

When a = 3 & b = 6

Equation of line :

x / 3 + y / 6 = 1

(2 x + y ) / 6 = 1

2 x + y = 6

2 x + y - 6 = 0

When a = 6 and b = 3

x / 6 + y / 3 = 1

( x + 2 y ) / 6 = 1

x + 2 y = 6

x + 2 y - 6 = 0.

Hence , we get answer.