Lesson Objective: I will be able to … Graph and solve linear inequalities in two variables Language Objective: I will be able to … Read, write, and listen about vocabulary, key concepts, and examples

Page 24 A linear inequality is similar to a linear equation, but the equal sign is replaced with an inequality symbol. A solution of a linear inequality is any ordered pair that makes the inequality true.

Example 1: Identifying Solutions of Inequalities Page 26 Tell whether the ordered pair is a solution of the inequality. (–2, 4); y < 2x + 1 y < 2x + 1 4 2(–2) + 1 Substitute (–2, 4) for (x, y). 4 –4 + 1 4 –3 <  (–2, 4) is not a solution.

Your Turn 1 Page 26 Tell whether the ordered pair is a solution of the inequality. (4, 5); y > x + 1 y > x + 1 5 4 + 1 5 5 > Substitute (4, 5) for (x, y).  (4, 5) is not a solution.

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Graphing Linear Inequalities Page 25 Graphing Linear Inequalities Step 1 Solve the inequality for y (slope-intercept form). Step 2 Graph the boundary line. Use a solid line for ≤ or ≥. Use a dashed line for < or >. Step 3 Shade the half-plane above the line for y > or ≥. Shade the half-plane below the line for y < or y ≤. Check your answer.

Example 2: Graphing Linear Inequalities in Two Variables Page 27 Graph the solutions of the linear inequality. y  2x – 3 Step 1 The inequality is already solved for y. Step 2 Graph the boundary line y = 2x – 3. Use a solid line for . Step 3 The inequality is , so shade below the line. Check y  2x – 3 0 2(0) – 3 0 –3   The point (0, 0) is a good test point to use if it does not lie on the boundary line. Helpful Hint

Your Turn 2 Graph the solutions of the linear inequality: Page 28 Graph the solutions of the linear inequality: 4x – 3y > 12 Step 2 Graph the boundary line y = – 4. Use a dashed line for <. Step 1 Solve the inequality for y. 4x – 3y > 12 –4x –4x –3y > –4x + 12 y < – 4 Check y < – 4 –6 (1) – 4 –6 – 4 –6 < 

Example 3: Writing an Inequality from a Graph Page 28 Write an inequality to represent the graph. y-intercept: 1; slope: Write an equation in slope-intercept form. The graph is shaded above a dashed boundary line. Replace = with > to write the inequality

Write an inequality to represent the graph. Your Turn 3 Page 29 Write an inequality to represent the graph. y-intercept: 0 slope: –1 Write an equation in slope-intercept form. y = mx + b y = –1x The graph is shaded below a dashed boundary line. Replace = with < to write the inequality y < –x.

Homework Assignment #35 Holt 6-5 #12, 13, 15, 19-21, 23, 26, 63