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Welcome to Unit 2: Linear and Exponential Relationships

Welcome to Unit 2: Linear and Exponential Relationships . Take out 3 pieces of binder paper . You Are Done with Unit 1…Now What?. Tomorrow ends Progress Report 1 (first 6 weeks of school) What did you think about Unit 1?. If it was Hard…. PLEASE come in for help!!

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Welcome to Unit 2: Linear and Exponential Relationships

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  1. Welcome to Unit 2: Linear and Exponential Relationships • Take out 3 pieces of binder paper

  2. You Are Done with Unit 1…Now What? • Tomorrow ends Progress Report 1 (first 6 weeks of school) • What did you think about Unit 1?

  3. If it was Hard… • PLEASE come in for help!! • My goal is for every student in this class to get an A, B, or C in my class!!! Let’s Make it Happen!!!!

  4. Goals for the next 6 weeks • I have done a lot of reflection about Unit 1 • I think it is important for us to make goals

  5. Follow the format: • I will_______________ by _________________. • Don’t make them unreasonable or unachievable!

  6. My goals as a Teacher • I will update grades once a week on IC by doing it on Friday before I leave school. • I will not rush through material until I feel like most of my students are ready to move on by checking for 80% accuracy during the lesson

  7. Now your turn! • I want you to make goals for the next 6 weeks • Turn in homework every day? • Study for quizzes? • Write something that YOU can do!

  8. Examples • Example: • Student who only does homework once a week: • “I will do my math homework 3-4 days a week by doing it right when I get home from school.” • Non-Example • I will get an A.

  9. Your turn • Think about your goals. I want you to write 2-3 goals for the next 6 weeks. • Write two copies of the SAME goals. • One is for me to keep • The other is for you to keep in your binder.

  10. Whiteboards Graph each inequality. 1. x > –5 2.y ≤ 0 3. Graph. y = 3x – 2

  11. Learning Objective • SWBAT graph linear inequalities

  12. Math Joke of the Day • Why were the math students getting up and sprinting around the room? • Their teacher kept saying “rise” and “run”

  13. Investigation

  14. Please Note:

  15. Vocabulary • Linear inequality • Describes a region of the coordinate plane that has a boundary line • Solution of an inequality • Coordinates of the plane that makes the inequality true

  16. y < 2x + 1 4 2(–2) + 1 4 –4 + 1  4 –3 < Example 1: In Notes Tell whether the ordered pair is a solution of the inequality. (–2, 4); y < 2x + 1 Substitute (–2, 4) for (x, y). (–2, 4) is not a solution.

  17. y > x − 4 1 3 – 4 > 1 – 1 Whiteboards Tell whether the ordered pair is a solution of the inequality. (3, 1); y > x –4 Substitute (3, 1) for (x, y).  (3, 1) is a solution.

  18. Dotted Line vs. Solid Line • Dotted boundary line • Not a solution • > < • Solid Boundary Line • Is a solution

  19. Shade Above or Below? • Shade above • When y > • Shade below • When y <

  20. Solve the inequality for y (slope-intercept form). ( y=mx+b) 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

  21. Example 2: Write in your Notes 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.

  22. Whiteboards • How do you know when you shade above or below the boundary line? • When do you use a dotted boundary line? • When do you use a solid boundary line?

  23. Step 2 Graph the boundary line . Use a solid line for ≥. = Whiteboard Graph the solutions of the linear inequality. Check your answer. Step 1 The inequality is already solved for y. Step 3 The inequality is ≥, so shade above the line.

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

  25. y-intercept: –5 slope: Replace = with ≤ to write the inequality Whiteboard Write an inequality to represent the graph. Write an equation in slope-intercept form. The graph is shaded below a solid boundary line.

  26. Special Cases • Y> 3 • Zero slope • X< -2 • Undefined slope

  27. Slope Dude • http://www.youtube.com/watch?v=ZzU8x5cMR-w

  28. 5x + 2y > –8 –5x –5x 2y > –5x –8 y= x – 4. y > x – 4 Step 2 Graph the boundary line Use a dashed line for >. Ex 4: Graphing in Standard Form Write this in your notes Graph the solutions of the linear inequality. Check your answer. 5x + 2y > –8 Step 1 Solve the inequality for y.

  29. Example 4 Continued Graph the solutions of the linear inequality. Check your answer. 5x + 2y > –8 Step 3 The inequality is >, so shade above the line.

  30. Whiteboards Graph the solutions of the linear inequality. Check your answer. 4x – y + 2 ≤ 0 Step 1 Solve the inequality for y. 4x – y + 2 ≤ 0 –y ≤ –4x – 2 –1 –1 y ≥ 4x + 2 Step 2 Graph the boundary line y = 4x + 2. Use a solid line for ≥.

  31. Whiteboards \ Graph the solutions of the linear inequality. Check your answer. Step 3 The inequality is ≥, so shade above the line.

  32. Word Problem!: Notes Ada has at most 285 beads to make jewelry. A necklace requires 40 beads, and a bracelet requires 15 beads. a. Write a linear inequality to describe the situation. Let x represent the number of necklaces and y the number of bracelets. Write an inequality. Use ≤ for “at most.”

  33. Necklace beads bracelet beads 285 beads. is at most plus 40x + 15y ≤ 285 40x + 15y ≤ 285 –40x –40x 15y ≤ –40x + 285 Word Problem!: Notes Cont’d Solve the inequality for y. Subtract 40x from both sides. Divide both sides by 15.

  34. Step 1 Since Ada cannot make a negative amount of jewelry, the system is graphed only in Quadrant I. Graph the boundary line . Use a solid line for ≤. = Word Problem!: Notes Cont’d b. Graph the solutions.

  35. Word Problem!: Notes Cont’d b. Graph the solutions. Step 2 Shade below the line. Ada 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 Ada can make.

  36. (2, 8)   (5, 3) Word Problem!: Notes Cont’d c. Give two combinations of necklaces and bracelets that Ada could make. Two different combinations of jewelry that Ada could make with 285 beads could be 2 necklaces and 8 bracelets or 5 necklaces and 3 bracelets.

  37. Whiteboards 1. You can spend at most $12.00 for drinks at a picnic. Iced tea costs $1.50 a gallon, and lemonade costs $2.00 per gallon. Write an inequality to describe the situation. Graph the solutions, describe reasonable solutions, and then give two possible combinations of drinks you could buy. 1.50x + 2.00y ≤ 12.00

  38. Whiteboards 1.50x + 2.00y ≤ 12.00 Only whole number solutions are reasonable. Possible answer: (2 gal tea, 3 gal lemonade) and (4 gal tea, 1 gal lemonde)

  39. Whiteboards 2. Write an inequality to represent the graph.

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