Graphing Inequalities in Two Variables
The solution set for an inequality in two variables contains
ordered pairs whose graphs fill an area on the coordinate plane
called a halfplane. An equation defines the boundary or edge of
the halfplane.
Graphing Inequalities in Two
Variables 
 Find the boundary by graphing the equation
related to the inequality. If the inequality
symbol is < or >, draw the boundary as a
dashed line. If the inequality symbol is or , draw the boundary as a
solid line to show that the points on the
boundary are included in the solution set.
 Determine which of the two halfplanes contains
the solutions by choosing a point in each
halfplane and testing its coordinates in the
inequality. If the coordinates make the
inequality true, shade that halfplane.

Example
Graph y  2 x 1.
Solution
Solve the inequality for y: y  2x 1. Then, graph the related equation y = 2x + 1. Draw
the line as a solid line since the inequality symbol is less than
or equal to. Select a point in each of the halfplanes and test
it in the inequality.
Test (0, 0) 
Test (1, 1) 
y  2x 1 
y  2x 1 
0  2(0) 1 
1  2(1) 1 
0 1 
True 
3 1 
False 
Therefore, the halfplane that contains the point (0, 0)
should be shaded.
