document.write( "Question 1124546: graph |x|-|y|=2 \n" ); document.write( "

Algebra.Com's Answer #740842 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "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.

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document.write( "quadrant I:    x>=0; y>=0: |x|=x;  |y|=y.   x-y = 2   -->  y =  x-2  (red line on graph below)\r\n" );
document.write( "quadrant II:   x<0;  y>=0: |x|=-x; |y|=y.  -x-y = 2   -->  y = -x-2  (blue line on graph below)\r\n" );
document.write( "quadrant III:  x<0;  y<0:  |x|=-x; |y|=-y. -x+y = 2   -->  y =  x+2  (black line on graph below)\r\n" );
document.write( "quadrant IV:   x>=0; y<0:  |x|=x;  |y|=-y.  x+y = 2   -->  y = -x+2  (green line on graph below)\r\n" );
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