SOLUTION: Graph the solution set of 3x-y<=-3

Algebra ->  Graphs -> SOLUTION: Graph the solution set of 3x-y<=-3      Log On


   

Question 110727: Graph the solution set of 3x-y<=-3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
In order to graph 3x-y%3C=-3, we need to graph the equation 3x-y=-3 (just replace the inequality sign with an equal sign).
So lets graph the line 3x-y=-3 (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%2B3%29+ graph of 3x-y=-3
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-y%3C=-3 with the test point

Substitute (0,0) into the inequality
3%280%29-%280%29%3C=-3 Plug in x=0 and y=0
0%3C=-3 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 not true, we do not shade the entire region that contains (0,0). So this means we shade the region that is on the opposite side of the line
Graph of 3x-y%3C=-3 with the boundary (which is the line 3x-y=-3 in red) and the shaded region (in green)