You can
put this solution on YOUR website!
The nature of the graph is going to change when either of the expressions in the absolute value signs change sign. Since those expressions change sign when either x or y changes sign, the nature of the graph will be different in each of the four quadrants.
quadrant I: x>=0; y>=0: |x|=x; |y|=y. x-y = 2 --> y = x-2 (red line on graph below)
quadrant II: x<0; y>=0: |x|=-x; |y|=y. -x-y = 2 --> y = -x-2 (blue line on graph below)
quadrant III: x<0; y<0: |x|=-x; |y|=-y. -x+y = 2 --> y = x+2 (black line on graph below)
quadrant IV: x>=0; y<0: |x|=x; |y|=-y. x+y = 2 --> y = -x+2 (green line on graph below)
