SOLUTION: graph each of the following inequalities on the cartesian plane 2x + y <_ -5 How do I know what number to plug in? Can I used any set of numbers? Do I have to make the statemen

Algebra ->  Graphs -> SOLUTION: graph each of the following inequalities on the cartesian plane 2x + y <_ -5 How do I know what number to plug in? Can I used any set of numbers? Do I have to make the statemen      Log On


   

Question 112885: graph each of the following inequalities on the cartesian plane
2x + y <_ -5
How do I know what number to plug in? Can I used any set of numbers? Do I have to make the statement true then graph it?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
In order to graph 2x%2By%3C=-5, we need to graph the equation 2x%2By=-5 (just replace the inequality sign with an equal sign).
So lets graph the line 2x%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+-2x-5%29+ graph of 2x%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 2x%2By%3C=-5 with the test point

Substitute (0,0) into the inequality
2%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 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 2x%2By%3C=-5 with the boundary (which is the line 2x%2By=-5 in red) and the shaded region (in green)