SOLUTION: graph the inequality 4x+5y<16

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Question 124723: graph the inequality
4x+5y<16
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
In order to graph 4x%2B5y%3C16, we need to graph the equation 4x%2B5y=16 (just replace the inequality sign with an equal sign).
So lets graph the line 4x%2B5y=16 (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+-%284%2F5%29x%2B%2816%2F5%29%29+ graph of 4x%2B5y=16
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 4x%2B5y%3C16 with the test point

Substitute (0,0) into the inequality
4%280%29%2B5%280%29%3C16 Plug in x=0 and y=0
0%3C16 Simplify





Since this inequality is true, we simply shade the entire region that contains (0,0)
Graph of 4x%2B5y%3C16 with the boundary (which is the line 4x%2B5y=16 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)