Graph the inequality.
2x + 3y > 6

First draw the graph of the boundary line,
whose equation is same as the inequality
with and equal sign replacing the " > ".

We get two points. The two intercepts are the
easiest to get (0,2) and (3,0).  Then we plot
those and draw a dotted line through them.



Now we must decide which side of the dotted line to
shade, by these rules.

1. If the coefficient of x is positive:
   A. Shade the side to the right the line if the inequality is 
      either ">" or ">
   B. Shade the side to the left of the line if the inequality is 
      either "<" or "<
2. If the coefficient of x is negative:
   A. Shade the side to the left of the line if the inequality is 
      either ">" or ">
   B. Shade the side to the right of the line if the inequality is 
      either "<" or "<
3. If the coefficient of y is positive:
   A. Shade the upper side of the line if the inequality is 
      either ">" or ">
   B. Shade the lower side of the line if the inequality is 
      either "<" or "<
4. If the coefficient of y is negative:
   A. Shade the lower side of the line if the inequality is 
      either ">" or ">
   B. Shade the upper side of the line if the inequality is 
      either "<" or "<

2x + 3y > 6

In this case, both coefficients are positive and the inequality
is " > ", so both 1.A. and 3.A. apply so we shade the side which 
is both above and to the right side of the line. 




Edwin