Take a look at the function [tex]y+2=- \frac{2}{3}x+4 [/tex]. You can simplify it to [tex]y=- \frac{2}{3}x+2 [/tex]. If x=0, then y=2 and when y=0, x=3. You obtain two points (0,2) and (3,0) that lie on the line [tex]y+2=- \frac{2}{3}x+4 [/tex].
Since [tex]y+2\le - \frac{2}{3}x+4 [/tex], the line [tex]y+2=- \frac{2}{3}x+4 [/tex] should belong to the shaded area.
Now take point (0,0). Since [tex]0+2\le- \frac{2}{3}\cdot 0+4 [/tex], you can conclude that point (0,0) belongs to the shaded area.Using all these thoughts, you can make a conclusion that the correct choice is B.
