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

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A) -2.5

B) -2

C) -1.5

D) -1

A) -2.5

B) -2

C) -1.5

D) -1

##### 2 Answers

Sum of slopes is

#### Explanation:

A line passing through point

or

or

or **(intercept form of equation)**

Observe that such a line forming a triangle in

and its

and hence area of triangle so formed is

or

or

or

or

i.e.

Hence sum of slopes is

and lines are

graph{(x+2y-6)(2x+y-6)=0 [-6.69, 13.31, -2.62, 7.38]}

#### Explanation:

Let, the **X-intercept** and **Y-intercept** of the line, say

point

Clearly,

Observe that, **Axes,** such a **right-triangle,**

of which, the lengths of the sides making the right angle are

Hence, the **area** of the right-triangle is

Knowing that,

Then,

These give