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 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.
|
