May 23rd
May 23rd
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.
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| 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.
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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.
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