SOLUTION: I just need to remember how to graph an inequality like this: 2x

SOLUTION: I just need to remember how to graph an inequality like this: 2x - 3y > 6

Question 119155: I just need to remember how to graph an inequality like this:
2x - 3y > 6

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
In order to graph , we need to graph the equation (just replace the inequality sign with an equal sign).
So lets graph the line (note: if you need help with graphing, check out this solver )
graph of
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 with the test point

Substitute (0,0) into the inequality
Plug in and
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 with the boundary (which is the line in red) and the shaded region (in green)
(note: since the inequality contains a greater-than sign, this means the boundary is excluded. This means the solid red line is really a dashed line)

RELATED QUESTIONS
2X-3y=6 I cannot remember how to solve this prob to graph. Thanjs for your help. (answered by rfer,josmiceli)