Graphing a Linear InequalityExample 2

Graph 3.2xy >–

STEP 1 Change > to and write the equation in slope-intercept form.

=

32xy =– Replace > with = sign.

Graph the line with slope 2 and y-intercept 3. Because the inequality symbol is >, use a dashed line.

2x= + 3 Add 2x to each side. y

Graphing a Linear InequalityExample 2

STEP 2 Test the point . Substitute the point into the original inequality.

32x y >–

( )0, 0

STEP 3 Shade the half-plane that does not contain .( )0, 0

320 – ( )0?>

30 is not a solution.( )0, 0>

Writing a Linear InequalityExample 3

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.

ART SUPPLIES

SOLUTION

Use a verbal model to write the inequality. Letx represent the number of tubes of paint and lety represent the number of brushes.

6 • x + 4 • y ≤ 40

Writing a Linear InequalityExample 3

ANSWERThe inequality 404y6x ≤+ models the situation.

Using the Graph of a Linear InequalityExample 4

Graph the inequality in Example 3. How many tubes of paint and how many brushes can you buy?

STEP 1 Change ≤ to and write the equation inslope-intercept form:

=

SOLUTION

10.y += –23 x

Graph the equation usinga solid line.

Using the Graph of a Linear InequalityExample 4

STEP 2 Test the point ( ): 0, 0 6( )0 + 4( )0?≤ 40

≤ 400

STEP 3 Shade the half-plane that contains( ).0, 0

ANSWER

Many solutions are possible, such as and You could buy 4 tubes of paint and 4 brushes or 2 tubes of paint and 5 brushes.

( )4, 4 ( ).2, 5

Guided Practice for Examples 2, 3, and 4

5. 1xy +<

Graph the inequality.

ANSWER

Guided Practice for Examples 2, 3, and 4

Graph the inequality.6. 3y3x ≥+

ANSWER

Guided Practice for Examples 2, 3, and 4

Graph the inequality.7. x – 12y ≤ –

ANSWER

Guided Practice for Examples 2, 3, and 4

Graph the inequality.8. y > 2–

ANSWER

Guided Practice

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.

for Examples 2, 3, and 4

ANSWER36;4y6x ≤+

Sample answer: 6 tubes of paint and 0 brushes, or 0 tubes of paint and 9 brushes.