Answer: D
Step-by-step explanation:
Let say a: the line decreasing
b: the line increasing
[tex]a: \ is\ passing\ through\ (0,2)\ and\ (2,-2)\\has \ the \ slope=\frac{2+2}{0-2} =-2\\its\ equation\ is\ y-2=-2(x-0) \ or\ y=-2x+2\ or\ 2x+y-2=0 \\for\ (0,0): -2 <=0\\\\\boxed{First\ region\ is\ y\leq -2x+2}\\\\[/tex]
[tex]b:\ is\ passing\ through\ (2,0)\ and\ (-2,-2) \\has\ the\ slope \ = \frac{-2-0} {-2-2} =\frac{1} {2} \\its\ equation\ is\ y-0=\frac{1}{2}(x-2)\ or\ y=\dfrac{x}{2}-1 \ or\ -x+2y+2=0\\for\ (0,0):\ +2 > 0\\\\\boxed{Second \ region\ is\ y\leq \dfrac{x}{2}-1 }\\[/tex]
Answer is D
