SOLUTION: Graph the solution to : 2x+3y<6

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Question 90004: Graph the solution to : 2x+3y<6
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

In order to graph 2x%2B3y%3C6, we need to graph the equation 2x%2B3y=6 (just replace the inequality sign with an equal sign).
So lets graph the line 2x%2B3y=6 (note: if you need help with graphing, check out this solver)

+graph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C+-%282%2F3%29x%2B2%29+ graph of 2x%2B3y=6
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 2x%2B3y%3C6 with the test point

Substitute (0,0) into the inequality
2%280%29%2B3%280%29%3C6 Plug in x=0 and y=0
0%3C6 Simplify

Since this inequality is true, we simply shade the entire region that contains (0,0)
Graph of 2x%2B3y%3C6 with the boundary (which is the line 2x%2B3y=6 in red) and the shaded region (in green)
(note: since the inequality contains a less-than sign, this means the boundary is excluded. This means the solid red line is really a dashed line)