A line passes through `(2,2)` and cuts a triangle of area `9` square units from the and cuts a triangle of area `9` square units from the first quadrant. The sum of all possible values for the slope of such a line, is-

Options

A. `-5//2`
B. `-2`
C. `-3//2`
D. `-1`

Answer

1

Explanation

Let line is `(x)/(a)+(Y)/(b)=1`
`:' ` it passes through (2,2)
`implies (2)/(a)+(2)/(b)=1 " "……(1)`
`:'` Aera of triangle `=(1)/(2)|ab|`
`9=(1)/(2)|ab|implies ab =18`
Solving (i) & (ii)
a=6 and a=3
b=3 b=6
slope of line is `-b/a`
i.e.`-2,-1/2`