SOLUTION: Please Help! Graph the inequality and shade in the correct area of the graph: 2/3x + 3y is less than or equal to 12

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Question 102656This question is from textbook
: Please Help!
Graph the inequality and shade in the correct area of the graph:
2/3x + 3y is less than or equal to 12 This question is from textbook

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Start with the given inequality

Multiply both sides by 3 to eliminate any fractions

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, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality with the test point

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)