SOLUTION: Graph the inequality on a plane 4x+5y<=20

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Question 146412: Graph the inequality on a plane
4x+5y<=20
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
4x%2B5y%3C=20 Start with the given inequality.


4x%2B5y=20 Replace the inequality sign with an equals sign.


5y=20-4x Subtract 4x from both sides.


y=%2820-4x%29%2F%285%29 Divide both sides by 5 to isolate y.




y=-%284%2F5%29x%2B4 Rearrange the terms and simplify.


So in order to plot 4x%2B5y%3C=20 or y%3C=-%284%2F5%29x%2B4 (which is the same thing), we need to plot the equation y=-%284%2F5%29x%2B20 first.
(note: if you need help with graphing, check out this solver)


+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%284%2F5%29x%2B4%29+ Graph of y=-%284%2F5%29x%2B4


Now plug in a test point (0,0) into the inequality y%3C=-%284%2F5%29x%2B20


y%3C=-%284%2F5%29x%2B4 Start with the given inequality.


0%3C=-%284%2F5%29%2A%280%29%2B4 Plug in x=0 and y=0


0%3C=4 Evaluate and simplify.


Since the inequality is true, this means that we shade the entire region that contains the point (0,0)


In other words, we simply shade the entire region that is below the line.

drawing%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%2C-%284%2F5%29x%2B4%2B-3%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%2C-%284%2F5%29x%2B4%2B-6%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%2C-%284%2F5%29x%2B4%2B-9%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%2C-%284%2F5%29x%2B4%2B-12%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%2C-%284%2F5%29x%2B4%2B-15%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%2C-%284%2F5%29x%2B4%2B-18%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%2C-%284%2F5%29x%2B4%2B-21%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%2C-%284%2F5%29x%2B4%2B-24%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%2C-%284%2F5%29x%2B4%2B-27%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%2C-%284%2F5%29x%2B4%2B-30%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%2C-%284%2F5%29x%2B4%2B-33%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%2C-%284%2F5%29x%2B4%2B-36%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%2C-%284%2F5%29x%2B4%2B-39%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%2C-%284%2F5%29x%2B4%2B-42%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%2C-%284%2F5%29x%2B4%2B-45%29%2C%0D%0Agraph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C-%284%2F5%29x%2B4%2C-%284%2F5%29x%2B4%2B-48%29%29 Graph of y%3C=-%284%2F5%29x%2B4 with the shaded region in green