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Review Linear Equations

This review focuses on the creation of linear equations based on real-life situations, specifically examining the relationship between the amount of chocolate eaten and overall happiness. We analyze the happiness levels experienced by Ada after consuming different quantities of chocolate bars and derive an equation that represents this relationship. Additionally, we explore parallel and perpendicular lines using the context of paths taken by individuals, helping to reinforce concepts in linear equations and their graphical representations.

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Review Linear Equations

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  1. Review Linear Equations Thursday, April 24th

  2. Review: Creating Equations Let’s assume that there is a linear relationship between amount of chocolate eaten and overall happiness. When Ada has eaten 1 chocolate bar, she feels an overall happiness of 5 smiles. When she has eaten 3 chocolate bars, she feels an overall happiness of 6 smiles. Create an equation for happiness as a function of chocolate bars eaten.

  3. Review: Creating Equations When Ada has eaten 1 chocolate bar, she feels an overall happiness of 5 smiles. When she has eaten 3 chocolate bars, she feels an overall happiness of 6 smiles. Create an equation for happiness as a function of chocolate bars eaten. Happiness Number of chocolate bars eaten

  4. Review: Creating Equations When Ada has eaten 1 chocolate bar, she feels an overall happiness of 5 smiles. When she has eaten 3 chocolate bars, she feels an overall happiness of 6 smiles. Create an equation for happiness as a function of chocolate bars eaten. (1, 5) Happiness Number of chocolate bars eaten

  5. Review: Creating Equations When Ada has eaten 1 chocolate bar, she feels an overall happiness of 5 smiles. When she has eaten 3 chocolate bars, she feels an overall happiness of 6 smiles. Create an equation for happiness as a function of chocolate bars eaten. (3, 6) (1, 5) Happiness Number of chocolate bars eaten

  6. Review: Creating Equations When Ada has eaten 1 chocolate bar, she feels an overall happiness of 5 smiles. When she has eaten 3 chocolate bars, she feels an overall happiness of 6 smiles. Create an equation for happiness as a function of chocolate bars eaten. (3, 6) (1, 5) Happiness Number of chocolate bars eaten

  7. Review: Creating Equations When Ada has eaten 1 chocolate bar, she feels an overall happiness of 5 smiles. When she has eaten 3 chocolate bars, she feels an overall happiness of 6 smiles. Create an equation for happiness as a function of chocolate bars eaten. (3, 6) Slope = ? (1, 5) Happiness Number of chocolate bars eaten

  8. Review: Creating Equations When Ada has eaten 1 chocolate bar, she feels an overall happiness of 5 smiles. When she has eaten 3 chocolate bars, she feels an overall happiness of 6 smiles. Create an equation for happiness as a function of chocolate bars eaten. (3, 6) Slope = ½ (1, 5) Happiness Number of chocolate bars eaten

  9. Review: Creating Equations When Ada has eaten 1 chocolate bar, she feels an overall happiness of 5 smiles. When she has eaten 3 chocolate bars, she feels an overall happiness of 6 smiles. Create an equation for happiness as a function of chocolate bars eaten. (3, 6) Slope = ½ (1, 5) Equation: y = ½x + b Happiness Number of chocolate bars eaten

  10. Review: Creating Equations When Ada has eaten 1 chocolate bar, she feels an overall happiness of 5 smiles. When she has eaten 3 chocolate bars, she feels an overall happiness of 6 smiles. Create an equation for happiness as a function of chocolate bars eaten. (3, 6) Slope = ½ (1, 5) Equation: y = ½x + b 5 = ½(1) + b Happiness Number of chocolate bars eaten

  11. Review: Creating Equations When Ada has eaten 1 chocolate bar, she feels an overall happiness of 5 smiles. When she has eaten 3 chocolate bars, she feels an overall happiness of 6 smiles. Create an equation for happiness as a function of chocolate bars eaten. (3, 6) Slope = ½ (1, 5) Equation: y = ½x + b 5 = ½(1) + b 9/2 = b Happiness Number of chocolate bars eaten

  12. Review: Creating Equations When Ada has eaten 1 chocolate bar, she feels an overall happiness of 5 smiles. When she has eaten 3 chocolate bars, she feels an overall happiness of 6 smiles. Create an equation for happiness as a function of chocolate bars eaten. (3, 6) Slope = ½ (1, 5) Equation: y = ½x + b 5 = ½(1) + b 9/2 = b y = ½x + 9/2 Happiness Number of chocolate bars eaten

  13. Parallel and Perpendicular Lines Matthew is walking down Keil drive, following the line: y = ¾x – 1 Meanwhile, Josh is biking down LaCroix, which is parallel to Keil and passes through the point (4, 5) at the intersection of Park and LaCroix. What is the equation for Josh’s path?

  14. Parallel and Perpendicular Lines Matthew is walking down Keil drive, following the line: y = ¾x – 1 Meanwhile, Josh is biking down LaCroix, which is parallel to Keil and passes through the point (4, 5) at the intersection of Park and LaCroix. What is the equation for Josh’s path? Slope = ?

  15. Parallel and Perpendicular Lines Matthew is walking down Keil drive, following the line: y = ¾x – 1 Meanwhile, Josh is biking down LaCroix, which is parallel to Keil and passes through the point (4, 5) at the intersection of Park and LaCroix. What is the equation for Josh’s path? Slope = ¾

  16. Parallel and Perpendicular Lines Matthew is walking down Keil drive, following the line: y = ¾x – 1 Meanwhile, Josh is biking down LaCroix, which is parallel to Keil and passes through the point (4, 5) at the intersection of Park and LaCroix. What is the equation for Josh’s path? Slope = ¾ Equation: Y = ¾x + b

  17. Parallel and Perpendicular Lines Matthew is walking down Keil drive, following the line: y = ¾x – 1 Meanwhile, Josh is biking down LaCroix, which is parallel to Keil and passes through the point (4, 5) at the intersection of Park and LaCroix. What is the equation for Josh’s path? Slope = ¾ Equation: Y = ¾x + b 5 = ¾(4) + b

  18. Parallel and Perpendicular Lines Matthew is walking down Keil drive, following the line: y = ¾x – 1 Meanwhile, Josh is biking down LaCroix, which is parallel to Keil and passes through the point (4, 5) at the intersection of Park and LaCroix. What is the equation for Josh’s path? Slope = ¾ Equation: Y = ¾x + b 5 = ¾(4) + b b = 2 y = ¾x + 2

  19. Parallel and Perpendicular Lines Matthew is walking down Keil drive, following the line: y = ¾x – 1 Meanwhile, Josh is biking down LaCroix, which is parallel to Keil and passes through the point (4, 5) at the intersection of Park and LaCroix. What is the equation for Josh’s path? y = ¾x + 2 Where do Josh and Matthew meet?

  20. Parallel and Perpendicular Lines Matthew is walking down Keil drive, following the line: y = ¾x – 1 Meanwhile, Josh is biking down LaCroix, which is parallel to Keil and passes through the point (4, 5) at the intersection of Park and LaCroix. What is the equation for Josh’s path? y = ¾x + 2 Where do Josh and Matthew meet? Never! There are no intersections between parallel lines with different intercepts

  21. Parallel and Perpendicular Lines Matthew is walking down Keil drive, following the line: y = ¾x – 1 Meanwhile, Katie is unicycling down Park, which is perpendicular to Keil and passes through the point (4, 5) at the intersection of Park and LaCroix. What is the equation for Katie’s path?

  22. Parallel and Perpendicular Lines Matthew is walking down Keil drive, following the line: y = ¾x – 1 Meanwhile, Katie is unicycling down Park, which is perpendicular to Keil and passes through the point (4, 5) at the intersection of Park and LaCroix. What is the equation for Katie’s path?

  23. Parallel and Perpendicular Lines Matthew is walking down Keil drive, following the line: y = ¾x – 1 Meanwhile, Katie is unicycling down Park, which is perpendicular to Keil and passes through the point (4, 5) at the intersection of Park and LaCroix. What is the equation for Katie’s path? Slope = ?

  24. Parallel and Perpendicular Lines Matthew is walking down Keil drive, following the line: y = ¾x – 1 Meanwhile, Katie is unicycling down Park, which is perpendicular to Keil and passes through the point (4, 5) at the intersection of Park and LaCroix. What is the equation for Katie’s path? Slope = –4/3

  25. Parallel and Perpendicular Lines Matthew is walking down Keil drive, following the line: y = ¾x – 1 Meanwhile, Katie is unicycling down Park, which is perpendicular to Keil and passes through the point (4, 5) at the intersection of Park and LaCroix. What is the equation for Katie’s path? Slope = –4/3 Equation: y = –4/3x + b

  26. Parallel and Perpendicular Lines Matthew is walking down Keil drive, following the line: y = ¾x – 1 Meanwhile, Katie is unicycling down Park, which is perpendicular to Keil and passes through the point (4, 5) at the intersection of Park and LaCroix. What is the equation for Katie’s path? Slope = –4/3 Equation: y = –4/3x + b 5 = –4/3(4) + b

  27. Parallel and Perpendicular Lines Matthew is walking down Keil drive, following the line: y = ¾x – 1 Meanwhile, Katie is unicycling down Park, which is perpendicular to Keil and passes through the point (4, 5) at the intersection of Park and LaCroix. What is the equation for Katie’s path? Slope = –4/3 Equation: y = –4/3x + b 5 = –4/3(4) + b b = 31/3 y = –(4/3)x + 31/3

  28. Parallel and Perpendicular Lines Matthew is walking down Keil drive, following the line: y = ¾x – 1 Meanwhile, Katie is unicycling down Park, which is perpendicular to Keil and passes through the point (4, 5) at the intersection of Park and LaCroix. What is the equation for Katie’s path? y = –(4/3)x + 10.33 Where do Katie and Matthew meet?

  29. Parallel and Perpendicular Lines Matthew is walking down Keil drive, following the line: y = ¾x – 1 Meanwhile, Katie is unicycling down Park, which is perpendicular to Keil and passes through the point (4, 5) at the intersection of Park and LaCroix. What is the equation for Katie’s path? y = –(4/3)x + 10.33 Where do Katie and Matthew meet? (5.4, 3.1)

  30. Jigsaw Review • Make 5 teams of 4-5 people. Make sure you fully understand the problem in your section. • Make 4 teams of 4-5 people ensuring that one member of each original team is there. Teach your teach how to solve the problems in your section.

  31. Individual Review Ask all the questions!

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