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Learning Target:

Learn how to identify and graph proportional relationships, determine quadrants, find the constant of proportionality, and write equations from graphs, tables, and word problems.

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Learning Target:

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  1. Learning Target: I can… Identify a proportional relationship from a graph

  2. Graphing in the coordinate plane Every point is written in the form _________. x tells you how many units you move ________, y tells you how many units you move _______ or ________.

  3. Graph the points: A (2,5) Quadrant? _____ B ( , ) Quadrant? _____ C ( , ) Quadrant? _____ D ( , ) Quadrant? _____ E ( , ) Quadrant? _____ F ( , ) Quadrant? _____ G ( , ) Quadrant? _____ H ( , ) Quadrant? _____

  4. Proportional Definition: Equal _______________ or equal ____________________

  5. Test for Equivalent Ratios

  6. 1) Is the total number of books read proportional to the number of months spent as part of the book club?

  7. 2)

  8. 3)

  9. 4)

  10. 5)

  11. 6)

  12. Conclusion The two relationships in a graph are proportional if the line is ___________________ and goes through the __________________

  13. the ORIGIN!!!!!

  14. Clicker – A for yes (proportional), B for No (not proportional)

  15. Which graph shows a proportional relationship? A. C. Yes No B. D. No No

  16. Which graph shows a proportional relationship? B A D C

  17. Which graph shows a proportional relationship?

  18. Meaning of proportional relationships

  19. Part A On your answer document, draw a coordinate plane that uses only Quadrant 1. Label the x-axis and the y-axis on the grid. Plot the points (3, 2) and (9, 6). Then, draw a line through the points so that the line extends to the edges of your coordinate plane. Part B Write each given point as a ratio and show how the ratios are proportional. Show your work and explain your thinking. Part C What does your line indicate about the proportionality of the two points in relation to the origin? Explain your thinking. Part D Write a different point that is proportional to (9, 6). Explain how you determined the point.

  20. EXIT: Identify if each graph shows a proportional (P) relationship or a non-proportional (N) relationship

  21. Learning Target: I can… Identify the constant of proportionality

  22. Constant of Proportionality Same as the Unit Rate

  23. Constant of Proportionality?

  24. Similar Figures – Scale Factor

  25. EXIT Find the constant of proportionality for this table

  26. Learning Target: I can… Write an equation for a proportional relationship

  27. To write an equation for a proportional relationship: • Identify the _______________________________ or _______________ • Put it in the form y = _________, using your constant of proportionality as k.

  28. From a Table: What is the constant of proportionality of the table above? y = 2x is the equation!

  29. From a Table: What is the constant of proportionality of the table above? y = 4x is the equation!

  30. What is the constant of proportionality for the following table? A. 2 B. -2 C. -½ D. ½

  31. What is the constant of proportionality for the following table?

  32. 5) What is the constant of proportionality of the table above? Since y = kx Note k stays constant. y = ¼ x is the equation!

  33. 6) Is this a proportional relationship? If yes, give the constant of proportionality. Yes! k = 6/4 or 3/2 Equation? y = 3/2 x

  34. 7) Yes! k = 25/10 or 5/2 k = 10/4 or 5/2 Equation? y = 5/2 x

  35. 8)

  36. Is this a proportional relationship? If yes, give the constant of variation (k) and the equation. No! The k values are different!

  37. Graphs • Identify if the relationship is _______________: if the line is straight and goes through the _________________. • Pick out ______________ and set up a _______. • Identify the constant of variation and write in the form ____________.

  38. 1)

  39. 3)

  40. 4)

  41. Write from a word problem. Justin makes $40 for 5 hours of yard work. Write an equation to find the money made (m) after h hours.

  42. Exit – Write the equation for this graph

  43. Learning Target: I can… Write equations from graphs, tables, pictures and word problems

  44. Which of the following is a proportional relationship?

  45. Equation y = kx, where k is the constant of proportionality Equation _______

  46. The equation y = 10x represents the amount of money y Julio earns for x hours of work. Identify the constant of proportionality. Explain what it represents in this situation.

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