Question 125588
To graph an inequality, you need to find a line and then shade in the appropriate half-plane.


The line is found by replacing the inequality symbol with an equals sign and graphing the resulting line.  If you have 'or equals' in your inequality sign in the first place, then you will draw a solid line, otherwise draw a dashed line.


Once you have your line, you need to know which side of the line to shade.  Pick a point that is not on the line.  If it isn't on the line I usually pick (0,0) because the arithmetic is easy, but if the line passes through the origin, pick something different, like (1,1).


Substitute the x- and y-coordinates from the point you selected into your original inequality.  If the substitution results in a true statement, you have found the 'correct' side of the line.  Shade in that side.  On the other hand, if you get a false result, shade in the other side.


Here's a graph of the line {{{y=2x}}}


{{{drawing(400,400,-4,4,-4,4,grid(1),graph(400,400,-4,4,-4,4,2x))}}}


On your graph, you should make this a dashed line because 'or equal to' is not part of your original inequality.  Note that the point (1,1) is below and to the right of the line.


Substitute 1 for x and 1 for y in your inequality:  {{{1<2(1)}}}.  This is a true statement, so below right is the side to shade.


Had you chosen a point like (-1,0) (up left of the line) to test you would have gotten the false statement {{{0<-2}}}.