SOLUTION: I hope I have this in the right place. I need help please! Graph the inequality on a plane. 2x+3y < or equal to 6. Thanks for any help at all.

Algebra ->  Graphs -> SOLUTION: I hope I have this in the right place. I need help please! Graph the inequality on a plane. 2x+3y < or equal to 6. Thanks for any help at all.      Log On


   

Question 127905: I hope I have this in the right place. I need help please! Graph the inequality on a plane. 2x+3y < or equal to 6. Thanks for any help at all.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
In order to graph 2x%2B3y%3C=6, 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%3C=6 with the test point

Substitute (0,0) into the inequality
2%280%29%2B3%280%29%3C=6 Plug in x=0 and y=0
0%3C=6 Simplify



(note: for some reason, some of the following images do not display correctly in Internet Explorer. So I 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 2x%2B3y%3C=6 with the boundary (which is the line 2x%2B3y=6 in red) and the shaded region (in green)