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

##
A) -2.5

B) -2

C) -1.5

D) -1

A) -2.5

B) -2

C) -1.5

D) -1

##### 1 Answer

Oct 30, 2017

Answer is

#### Explanation:

Let the slope of the line be

Now, area of triangle in such a case is half the product of

Hence, if area of triangle is

or

or

or

As in a quadratic equation

sum of slopes is

graph{(x+2y-6)(y+2x-6)=0 [-1, 13, -0.5, 6.5]}