Labeling Assignments Title Heading 8.4: Graphing and Solving Linear Inequalities Last, First Date Period
8.4: Graphing and Solving Linear Inequalities
8EE: Standard 8. Analyze and solve pairs of simultaneous linear equations. b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations.
Introduction Tell whether the ordered pair is a solution of the inequality: 1. 7, 3 ; y < x 1 2. 4, 5 ; y > 3x + 2 3. 3, 2 ; y < x + 2 4. 4, 5 ; y > x 1
Introduction KEY Tell whether the ordered pair is a solution of the inequality: 1. 7, 3 ; y < x 1 2. 4, 5 ; y > 3x + 2 yes no 3. 3, 2 ; y < x + 2 4. 4, 5 ; y > x 1 yes no
So, what are inequalities? O Use the following link to learn the basics of inequalities: http://www.mathsisfun.com/algebra/inequality.html O Complete the ten problems at the bottom of page
Remember Linear Equations Slope Intercept Form O y = mx + b
Linear Inequalities
Introduction KEY Tell whether the ordered pair is a solution of the inequality: 1. 7, 3 ; y < x 1 2. 4, 5 ; y > 3x + 2 yes no 3. 3, 2 ; y < x + 2 4. 4, 5 ; y > x 1 yes no
Classwork: 8.4A Graph each inequality on Geogebra. Write down a coordinate pair that lies is the region and check. 1. y < x 1 2. y > 3x + 2 3. y x + 2 4. y x 1 5. y 4 6. y < 2 7. x 3 8. x > 5 9. What kind of line is used for < or >? for or? 10. How do you know what part of graph to shade?
Classwork: 8.4A KEY Graph each inequality on Geogebra. Write down a coordinate pair that lies is the region and check. 1. y < x 1 2. y > 3x + 2 1< 5-1 1< 4 1> 3(-1) 1 1> -3 1 1 > -4
Classwork: 8.4A KEY Graph each inequality on Geogebra. Write down a coordinate pair that lies is the region and check. 3. y x + 2 4. y x 1 3 1 +2 3 3 3 1 1 3 0
Classwork: 8.4A KEY Graph each inequality on Geogebra. Write down a coordinate pair that lies is the region and check. 5. y 4 6. y < 2 0 < 2-4 -4
Classwork: 8.4A KEY Graph each inequality on Geogebra. Write down a coordinate pair that lies is the region and check. 7. x 3 8. x > 5 0 3 0 > -5
Classwork: 8.4A KEY Graph each inequality on Geogebra. Write down a coordinate pair that lies is the region and check. 9. What kind of line is used for < or >? for or? For < or > you use a dashed (dotted) line; for or you use a solid line. 10. How do you know what part of graph to shade? You select a point in the region; if the point checks out, you shade that region; If not, shade the other region.
8.4: Solving Linear Inequalities O Log onto my.hrw.com and select the Algebra Textbook O Select Chapter 6 and press GO! O Click the Additional Practice Tab O Under Lesson Resources Click on O Lesson 6: Solving Linear Inequalities O Click on Homework Help Online O Watch the following video: O Lesson 6-6: Example 2
Classwork: 8.4B Solve the inequality for y. Graph each inequality. Use Geogebra to verify. Choose a coordinate pair and check. 1. 5x + 2y > 8 2. -4x + y -2 3. 4x 3y > 12 4. 2x y > 4 5. 2y 4 6. 3x < 6
Classwork: 8.4B KEY Solve the inequality for y. Graph each inequality. Use Geogebra to verify. Choose a coordinate pair and check. 1. 5x + 2y > 8 2. -4x + y -2 y > 5 2 x - 4 0 > 5 2 (0) 4 0 > - 4 y 4x - 2 0 4(1) 2 0 2
Classwork: 8.4B KEY Solve the inequality for y. Graph each inequality. Use Geogebra to verify. Choose a coordinate pair and check. 3. 4x 3y > 12 4. 2x y > 4 y < 4 3 x - 4 3 < 4 3 (6) 4 3 < 8 4 3 < 4 y < 2x - 4 0 < 2(3) 4 0 < 6 4 0 < 2
Classwork: 8.4B KEY Solve the inequality for y. Graph each inequality. Use Geogebra to verify. Choose a coordinate pair and check. 5. 2y 4 6. 3x < 6 y - 2 0 2 x > - 2 0 > 2
CW 8.4C - Groups O Create a student account in Prezi.com O Come up with a scenario for your problem O Create a Prezi
Application of Inequalities Jessyca has at most 285 beads to make jewelry. A necklace requires 40 beads, and a bracelet requires 15 beads. What is a combination of necklaces and bracelets that Jessyca can make? Let x = number of necklaces and y = number of bracelets. Write an inequality. Use for at most.
Necklace beads Application of Inequalities plus bracelet beads is at most 285 beads. 40x + 15y 285 Solve the inequality for y. 40x + 15y 285 40x 40x 15y 40x + 285 Subtract 40x from both sides. Divide both sides by 15.
Application of Inequalities b. Graph the solutions. Step 1 Since Jessyca cannot make a negative amount of jewelry, the system is graphed only in Quadrant I. Graph the boundary line. Use a solid line for. =
Application of Inequalities b. Graph the solutions. Step 2 Shade below the line. Jessyca can only make whole numbers of jewelry. All points on or below the line with whole number coordinates are the different combinations of bracelets and necklaces that Jessyca can make.
Application of Inequalities c. Give two combinations of necklaces and bracelets that Jessyca could make. Two different combinations of jewelry that Jessyca could make with 285 beads could be 2 necklaces and 8 bracelets or 5 necklaces and 3 bracelets. (2, 8) (5, 3)
Prodigi O http://www.mangahigh.com/enus/math_games/algebra/inequalities/inequ alities_on_graphs
CW 8.4C - Groups O Create a student account in Prezi.com Watch tutorial 1 Watch tutorial 2 Watch tutorial 3 O Brainstorm within your group O Create a Prezi O Get creative!
CW 8.4C Prezi ntation O Title O Introduction O Scenario with driving question O Word Model O Linear Inequality O Work O Graph O Conclusion O Get creative!
Classwork 8.4D O Log onto my.hrw.com and select the Algebra Textbook O Select Chapter 6 and press GO! O Click the Additional Practice Tab O Under Lesson Resources Click on O Lesson 6: Solving Linear Inequalities O Click on Homework Help Online O Complete 4 problems by clicking under: O Lesson 6-6: See Example 2
Questions?