The solution set for an inequality in two variables contains
ordered pairs whose graphs fill an area on the coordinate plane
called a half-plane. An equation defines the boundary or edge of
the half-plane.
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 half-planes contains
the solutions by choosing a point in each
half-plane and testing its coordinates in the
inequality. If the coordinates make the
inequality true, shade that half-plane.
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 half-planes 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 half-plane that contains the point (0, 0)
should be shaded.
or 
, draw the boundary as a
solid line to show that the points on the
boundary are included in the solution set. 