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Proportional vs. Non-Proportional Variation Challenge

Explore direct variation systems of equations, slopes, and solutions through engaging challenges and real-world scenarios. Test understanding with graphs and calculations.

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Proportional vs. Non-Proportional Variation Challenge

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  1. Proportional Vs Non-Proportional Direct Variation Systems of Equations y = mx + b CHALLENGE 1 pt 1 pt 1 pt 1 pt 1 pt 2 pt 2 pt 2 pt 2 pt 2 pt 3 pt 3 pt 3 pt 3 pt 3 pt 4 pt 4 pt 4 pt 4 pt 4 pt 5 pt 5 pt 5 pt 5 pt 5 pt

  2. 1 pt DV #1

  3. 2 pt What is x? DV #2

  4. 3 pt Every 3 hours, a machine produces 60 baskets. How many hours will it take to produce 100 baskets? DV #3

  5. 4 pt Carla is renting a canoe. It costs $80 for 2 hours and $160 for 4 hours. What is the rate per hour? DV #4

  6. The graph shows 2 objects moving at a constant speed. Find the speed of Object A in meters per second. 5 pt DV #5

  7. 1 pt Proportional or Non-proportional? P/NP #1

  8. 2 pt Does the following set of ordered pairs represent a proportional or Non-proportional relationship? P/NP #2

  9. Determine which relationship in each of the following “Quads” (sets of 4) represents a Non-proportional relationship. Write down its letter (A, B, C, or D). 3 pt P/NP #3

  10. 4 pt Determine which relationship in each of the following “Quads” (sets of 4) represents a Non-proportional relationship. Write down its letter (A, B, C, or D). P/NP #4

  11. 5 pt Determine which relationship in each of the following “Quads” (sets of 4) represents a Non-proportional relationship. Write down its letter (A, B, C, or D). P/NP #5

  12. 1 pt Slope #1

  13. 2 pt What is the slope of a line passing through (4, 3) and (3,1) ? Slope #2

  14. 3 pt Write the equation of the graphed line. Slope #3

  15. 4 pt Write the equation of the graphed line. Slope #4

  16. 5 pt Write the equation of the line from the table below. Slope #5

  17. 1 pt What is the solution to the system of equations below? SYSTEMS #1

  18. 2 pt What is the solution to the system of equations below? HINT: Complete two t-charts! SYSTEMS #2

  19. 3 pt What is the solution to the system of equations below? HINT: Complete two t-charts! SYSTEMS #3

  20. 4 pt What is the solution to the system of equations below? HINT: Complete two t-charts! SYSTEMS #4

  21. 5 pt Candy is sold by the ounce at two stands at the mall. One stand charges $1.50 per ounce in a free bag. A second stand charges $6 for a jar that you can fill for $0.75 per ounce. How many ounces must be bought for the cost of the bag of candy to equal the cost of the jar? _______ HINT: Complete two t-charts! SYSTEMS #5

  22. 1 pt Challenge #1

  23. 2 pt Challenge #2

  24. 3 pt • For a few months, Dexter recorded the amounts, in fluid ounces, of laundry detergent remaining, y, after he and his family washed x loads of laundry. The equation of the line of best fit for his data is shown below. • y = –1.6x + 50 • Which statement correctly describes the slope of Dexter’s equation of the line of best fit in the context of the situation? • The bottle Dexter’s family buys holds about 50 fluid ounces of detergent. • For each load of laundry, Dexter’s family uses about 1.6 fluid ounces of detergent. • With 50 fluid ounces of detergent, Dexter’s family can wash about 1.6 loads of laundry. • With 1.6 bottles of laundry detergent, Dexter’s family can wash about 50 loads of laundry Challenge #3

  25. 4 pt Challenge #4

  26. 5 pt Challenge #5

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