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Linear Inequalities in Two Variables 2-5
Warm Up Lesson Presentation Lesson Quiz Holt Algebra 2
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Warm Up Find the intercepts of each line. 1. 3x + 2y = 18
Write the function in slope-intercept form. Then graph. 4. 2x + 3y = –3 (0, 9), (6, 0) (0, –8), (2, 0) (0, 5), (–2, 0)
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Objectives Graph linear inequalities on the coordinate plane.
Solve problems using linear inequalities.
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Vocabulary linear inequality boundary line
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Linear functions form the basis of linear inequalities
Linear functions form the basis of linear inequalities. A linear inequality in two variables relates two variables using an inequality symbol, such as y > 2x – 4. Its graph is a region of the coordinate plane bounded by a line. The line is a boundary line, which divides the coordinate plane into two regions.
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Example 1A: Graphing Linear Inequalities
Graph the inequality The boundary line is which has a y-intercept of 2 and a slope of . Draw the boundary line dashed because it is not part of the solution. Then shade the region above the boundary line to show .
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Example 1A Continued Check Choose a point in the solution region, such as (3, 2) and test it in the inequality. ? 2 > 1 ? The test point satisfies the inequality, so the solution region appears to be correct.
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Example 1B: Graphing Linear Inequalities
Graph the inequality y ≤ –1. Recall that y= –1 is a horizontal line. Step 1 Draw a solid line for y=–1 because the boundary line is part of the graph. Step 2 Shade the region below the boundary line to show where y < –1. .
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Example 1B Continued Check The point (0, –2) is a solution because –2 ≤ –1. Note that any point on or below y = –1 is a solution, regardless of the value of x.
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Check It Out! Example 1a Graph the inequality y ≥ 3x –2. The boundary line is y = 3x – 2 which has a y–intercept of –2 and a slope of 3. Draw a solid line because it is part of the solution. Then shade the region above the boundary line to show y > 3x – 2.
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Check It Out! Example 1a Continued
Check Choose a point in the solution region, such as (–3, 2) and test it in the inequality. y ≥ 3x –2 2 ≥ 3(–3) –2 ? 2 ≥ (–9) –2 ? 2 > –11 ? The test point satisfies the inequality, so the solution region appears to be correct.
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Lesson Quiz: Part I 1. Graph 2x –5y 10 using intercepts. 2. Solve –6y < 18x – 12 for y. Graph the solution. y > –3x + 2
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Lesson Quiz: Part II 3. Potatoes cost a chef $18 a box, and carrots cost $12 a box. The chef wants to spend no more than $144. Use x as the number of boxes of potatoes and y as the number of boxes of carrots. a. Write an inequality for the number of boxes the chef can buy. 18x + 12y ≤ 144 b. How many boxes of potatoes can the chef order if she orders 4 boxes of carrot? no more than 5
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