Question 87406: Graph the inequality:
2x-3y is less then or equal to 12
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Start with the given system of inequalities
In order to graph this system of inequalities, we need to graph each inequality one at a time.
First lets graph the first inequality
In order to graph , we need to graph the equation  (just replace the inequality sign with an equal sign).
So lets graph the line (note: if you need help with graphing, check out this solver)
 graph of
Now lets pick a test point, say (0,0) (any point will work, but this point is the easiest to work with), and evaluate the inequality
Substitute (0,0) into the inequality
 Plug in  and 
 Simplify
Since this inequality is true, we simply shade the entire region that contains (0,0)
 Graph of with the boundary (which is the line in red) and the shaded region (in green)
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