SOLUTION: How do I determine the correct half-plane and complete the graph for y > 2x (there is an underline on greater than). Thanks.

Click here to see ALL problems on Linear-equations

Question 88015: How do I determine the correct half-plane and complete the graph for y > 2x (there is an underline on greater than). Thanks.
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
How do I determine the correct half-plane and complete the graph for y >= 2x (there is an underline on greater than).
--------------
First: Graph the line y=2x
Second: Select a point that is not on the line, for example (10,10)
Third: Substtute those x and y values into the INEQUALITY, as follows:
10 > 2*10
If that is a false statement the half-plane you want is not on that
side of the line; darken the half-plane on the other side of the line.
-------
If it is true darken the half-plane containing the point.
----------------------
Cheers,
Stan H.

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 (0,1). 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 (0,1) into the inequality
Plug in and
Simplify
Since this inequality is true, we simply shade the entire region that contains (0,1)
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 or equal sign, this means the boundary is included. So the region contains the boundary)

So essentially we shade the half plane that is above the line