SOLUTION: graph 5x+y<=5

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Question 93235: graph 5x+y<=5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
In order to graph 5x%2By%3C=5, we need to graph the equation 5x%2By=5 (just replace the inequality sign with an equal sign).
So lets graph the line 5x%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+-5x%2B5%29+ graph of 5x%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 5x%2By%3C=5 with the test point

Substitute (0,0) into the inequality
5%280%29%2B%280%29%3C=5 Plug in x=0 and y=0
0%3C=5 Simplify



(note: for some reason, some of the following images do not display correctly in Internet Explorer. So I would recommend the use of Firefox to see these images.)


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