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**5-5**Solving Linear Inequalities Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 1 Holt Algebra 1**Warm Up**Graph the inequality. 1. x > –5 2. Write –6x + 2y = –4 in slope-intercept form, and graph.**Warm Up**Graph each inequality. 1. x > –5 3. Write –6x + 2y = –4 in slope-intercept form, and graph. y = 3x – 2**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.**y < 2x + 1**4 2(–2) + 1 4 –4 + 1 4 –3 < I do…. Tell whether the ordered pair is a solution of the inequality. (–2, 4); y < 2x + 1 (–2, 4) is not a solution.**y > x − 4**1 3 – 4 > 1 – 1 We do…. (3, 1); y > x –4 Substitute (3, 1) for (x, y). (3, 1) is a solution.**1 1 – 7**5 4 + 1 55 < 1–6 > You do… a. (4, 5); y < x + 1 b. (1, 1); y > x – 7 y < x + 1 y > x – 7 (1, 1) is a solution. (4, 5) is not a solution.**We do…..**y = mx + b**We do…..**y = mx + b**We do…..**y = mx + b**A linear inequality describes a region of a coordinate plane**called a half-plane. All points in the region are solutions of the linear inequality.**Solve the inequality for y (slope-intercept form).**Step 1 Graph the boundary line. Use a solid line for ≤ or ≥. Use a dashed line for < or >. Step 2 Shade the half-plane above the line for y > or ≥. Shade the half-plane below the line for y < or y ≤. Check your answer. Step 3 Graphing Linear Inequalities**Example : Graphing Linear Inequalities in Two Variables**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.**Helpful Hint**The point (0, 0) is a good test point to use if it does not lie on the boundary line.**Example: Graphing Linear Inequalities in Two Variables**5x + 2y > –8**5x + 2y > -8**Y = mx + b**Check**y > x – 4 0(0) – 4 0 –4 0 –4 > Example Continued 5x + 2y > –8 Substitute ( 0, 0) for (x, y).**Use a Grapher**-Mathway grapher**Check It Out!**4x – y + 2 ≤ 0**Check It Out!**4x –3y > 12**Check It Out!**2x – y –4 > 0**y-intercept: –5 slope:**Replace = with ≤ Example : Writing an Inequality from a Graph Write an inequality to represent the graph.**Check It Out!**Write an inequality to represent the graph. y-intercept: 0 slope: –1 y < –x.**Check It Out!**Write an inequality to represent the graph. y-intercept: –3 slope: –2 y ≥ –2x – 3.**Lesson Quiz:**Write an inequality to represent the graph.