x-y < 2

Solve for y

 -y < 2-x

Divide through by the coefficient of y which is -1,
and since it is negative, the < becomes a >

  y > -2+x

  y > x-2

So we draw the equation of the boundary line y = x-2.  
We draw the line dotted since " > " does not include equality:



There are two ways to determine which side of the line
to shade.

1.  Since it is solved for y and it is "y > ", we shade
the area above the line.  [If it had been "y < " we would
have shaded the area below the line].

2.  Substitute any test point that is not on the line.  
Since the easiest test point is (0,0) substitute x=0 and y=0
into the original inequality to see whether the test point 
is in the solution set or not.

x-y < 2
0-0 < 2
  0 < 2

This is true so the origin is in the solution set, so we shade 
the side of the line which the test point (0,0) is on.  That
is the area above the line:



Edwin