SOLUTION: Graph the inequality. 3x + y < 5 with a line under the greater sighn

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Question 91291: Graph the inequality.
3x + y < 5 with a line under the greater sighn
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
In order to graph 3x%2By%3C5, we need to graph the equation 3x%2By=5 (just replace the inequality sign with an equal sign).
So lets graph the line 3x%2By=5 (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+-3x%2B5%29+ graph of 3x%2By=5
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 3x%2By%3C5 with the test point

Substitute (0,0) into the inequality
3%280%29%2B%280%29%3C5 Plug in x=0 and y=0
0%3C5 Simplify



Since this inequality is true, we simply shade the entire region that contains (0,0)
Graph of 3x%2By%3C5 with the boundary (which is the line 3x%2By=5 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)