Graphuing Linear Inequalities
To graph a linear inequality in x and y, you may find it helpful to first
solve the inequality for y. Once that has been done, the inequality can be
graphed using the following guidelines:
Inequality
y > mx + b
y ≥ mx + b
y < mx + b
y ≤ mx + b |
Solution
Draw a dotted line and shade the region above
the line.
Draw a solid line and shade the region above the
line.
Draw a dotted line and shade the region below
the line.
Draw a solid line and shade the region below the
line. |
Example 1
Graph the inequality 3x - 2y ≤ -12.
Solution
First, solve the inequality for y.
Subtract 3x from both sides.
Divide both sides by -2. Remember to
reverse the direction of the inequality
symbol. |
3x - 2y
2y
y |
≤ -12
≤ -3x - 12
≥
|
Next, graph the corresponding equation
The inequality has the form y ≥ mx
+ b, so draw a solid line.
Then, shade the region above the line.
It is a good idea to check the shading with a test point.
Substitute (0, 0) in 3x - 2y ≤ -12.
The result is 0 ≤ -12, which is false.
Since (0, 0) is not a solution, the region that contains (0, 0) should not be
shaded. This agrees with the graph as we have drawn it. |
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