Linear Inequalities in Two Variables 2-5 Warm Up Lesson Presentation Lesson Quiz Holt Algebra 2

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)

Objectives Graph linear inequalities on the coordinate plane. Solve problems using linear inequalities.

Vocabulary linear inequality boundary line

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.

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 .

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.

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. .

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.

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.

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.

Lesson Quiz: Part I 1. Graph 2x –5y  10 using intercepts. 2. Solve –6y < 18x – 12 for y. Graph the solution. y > –3x + 2

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