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

$(2,2)\in y=mx+c \to 2=2m+c \to c=2-2m,y=mx+2-2m$ intersects coordinate axes at A and B 
 $$\begin{gathered} Area of \Delta OAB=9 \\ \frac{c^2}{2\left|ab\right|}=9 \\ \frac{{\left(2-2m\right)}^2}{2\left|m\right|}=9 \\ 2(1+m^2-2m)=\pm 9m \\ 2m^2-13m+2=0, 2m^2+5m+2=0 \\ {m}_1+m_2=-\frac{5}{2}=-2.5 \end{gathered}$$