SOLUTION: hi i need some help with graphing inequalities i understand some of it, but not all of it. like for example i need help with y_< 2x+4

First graph just the boundary line, which is 
the line whose equation is just like the 
inequality except that it has an equal sign in
place of the inequality sign.  That is, the 
boundary line is the line whose equation is
 

Graph that line by finding a couple of points on it. 

Let x = 0
                  y = 2x + 4
                  y = 2(0) + 4
                  y = 0 + 4
                  y = 4

So one point is (0,4)

Let x = -2
                  y = 2x + 4
                  y = 2(-2) + 4
                  y = -4 + 4
                  y = 0

So another point is (-2,0)

Plot those untercepts and draw a line
through them:



Now we have to decide which side of that 
line we are to shade.

Arbitrarily pick a point on each side of 
the line. Substitute their coordinates for 
x and y in the original inequality.

Let's arbitrarily pick, say (3,2) on the 
right side of that line and substitute it
into






That is true, so we shade the entire right
side of the line which (3,2) is on.

Let's arbitrarily pick, say (-4,3) on the 
left side of that line and substitute it
into






That is false, so we do not shade the 
left side of the line which (-4,3) is on.

So we shade only the right side of the line.
I can't shade on here, so I'll just type 
"SHADE THIS SIDE" on the right side. 



What you should know about other
problems of this kind is that if
the inequality had beem strictly
less than, or strictly greater,
the line would not be included
in the graph and so you would
draw it dotted and not solid.

Shortcut 1:
You only need test one point.  If it
tests true in the original inequality,
then shade that side of the line and do
not shade the other side. If it tests
false, then do not shade that side but
instead shade the other side.

Shortcut 2:
Choose the origin (0,0) as a test point
whenever the line does not go through
the origin.  

Edwin