Graphing a Linear Inequality Example 2 Graph x2xy>– STEP 1 Change > to and write the equation in slope-intercept form. = 32x2xy = – Replace > with = sign. Graph the line with slope 2 and y -intercept 3. Because the inequality symbol is >, use a dashed line. 2x2x = +3 Add 2x to each side. y

Graphing a Linear Inequality Example 2 STEP 2 Test the point. Substitute the point into the original inequality. 32x2x 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 Inequality Example 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. Let x represent the number of tubes of paint and let y represent the number of brushes. 6x+4y ≤ 40

Writing a Linear Inequality Example 3 ANSWER The inequality 404y4y6x6x≤+ models the situation.

Using the Graph of a Linear Inequality Example 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 in slope-intercept form: = SOLUTION 10. y + = – 2 3 x Graph the equation using a solid line.

Using the Graph of a Linear Inequality Example 4 STEP 2 Test the point ( ):): 0, 0 6 () () 0 ? ≤ 40 ≤ 0 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 xy + < Graph the inequality. ANSWER

Guided Practice for Examples 2, 3, and 4 Graph the inequality. 6. 3y3x3x ≥ + ANSWER

Guided Practice for Examples 2, 3, and 4 Graph the inequality. 7. x – 12y2y≤ – 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 ANSWER 36 ; 4y4y6x6x≤+ Sample answer: 6 tubes of paint and 0 brushes, or 0 tubes of paint and 9 brushes.