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Example 2
Graphing a Linear Inequality
Graph y – 2x > 3.
STEP 1 Change > to = and write the equation in
slope-intercept form.
y – 2x = 3
y = 2x + 3
Replace > with = sign.
Add 2x to each side.
Graph the line with slope 2 and y-intercept 3.
Because the inequality symbol is >, use a dashed
line.
Example 2
Graphing a Linear Inequality
STEP 2 Test the point ( 0, 0).
Substitute the point into
the original inequality.
y – 2x > 3
?
(
)
0 – 20 > 3
0 > 3
(0, 0 ) is not a solution.
STEP 3 Shade the half-plane that does not contain ( 0, 0).
Example 3
Writing a Linear Inequality
ART SUPPLIES
You can spend at most $40 on art supplies. Tubes
of paint cost $6 each and brushes cost $4 each.
Write an inequality to model the situation.
SOLUTION
Use a verbal model to write the inequality. Let
x represent the number of tubes of paint and let
y represent the number of brushes.
6
•
x
+
4
•
y
≤
40
Example 3
Writing a Linear Inequality
ANSWER
The inequality 6x + 4y ≤ 40 models the situation.
Example 4
Using the Graph of a Linear Inequality
Graph the inequality in Example 3. How many tubes
of paint and how many brushes can you buy?
SOLUTION
STEP 1 Change ≤ to = and write
the equation in
slope-intercept form:
3
y = – x + 10.
2
Graph the equation using
a solid line.
Example 4
Using the Graph of a Linear Inequality
?
STEP 2 Test the point ( 0, 0): 6 ( 0) + 4 ( 0) ≤ 40
0 ≤ 40
STEP 3 Shade the half-plane that contains ( 0, 0).
ANSWER
Many solutions are possible, such as ( 4, 4) and ( 2, 5).
You could buy 4 tubes of paint and 4 brushes or 2 tubes
of paint and 5 brushes.
Guided Practice
Graph the inequality.
5. y < x + 1
ANSWER
for Examples 2, 3, and 4
Guided Practice
Graph the inequality.
6. 3x + y ≥ 3
ANSWER
for Examples 2, 3, and 4
Guided Practice
Graph the inequality.
7. x – 2y ≤ –1
ANSWER
for Examples 2, 3, and 4
Guided Practice
Graph the inequality.
8. y > – 2
ANSWER
for Examples 2, 3, and 4
Guided Practice
for Examples 2, 3, and 4
9. WHAT IF?
In Example 3, suppose you can spend at most $36.
Write and graph an inequality to model the situation.
Find two possible solutions.
ANSWER
6x + 4y ≤ 36;
Sample answer: 6 tubes of paint and 0 brushes, or 0
tubes of paint and 9 brushes.