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Constant of Proportionality

Constant of Proportionality. 7 th Grade Chapter 2. Standard. CC.7.RP.2b Identify the constant of proportionality in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Essential Question.

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Constant of Proportionality

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  1. Constant of Proportionality 7th Grade Chapter 2

  2. Standard CC.7.RP.2b Identify the constant of proportionality in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

  3. Essential Question How do I identify the constant of proportionality in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships?

  4. Remember:Unit Rate is… A ratio that has a denominator of one… showing the value of one unit. Examples: price per pound pages read in one hour cups that can fit on one shelf price per gallon

  5. Real World Application If a person walks 4 mile in 2 hours, what is the unit rate? (miles per hour) = 2 miles per hour

  6. Record your information in a table. The dependent variable depends on the independent variable in order to find its value. The independent variable does not depend on anything. Books Price 5 1 10 2 3 15 20 4 5 25 6 30

  7. Graph It! A straight line through the origin shows a direct proportion on a graph… As x is increasing, y is also increasing. 10 9 8 7 6 5 Price dependent 4 3 2 1 1 2 3 5 4 Books independent

  8. Proportionality The graph of a proportional relationship is a straight line that passes through the origin. Proportional quantities can be described by the equation y = kx, where k is a constant ratio... also known as constant of proportionality.

  9. Using the form y = kx, write an equation for the information in the chart. Books Price What did you multiply xto get y? 5x = y 5 1 10 2 3 15 20 4 5 25 6 30

  10. If y = kx then doesn’t k = y/x? 5x = y To find the constant of proportionality, you can divide the y coordinate by the x coordinate. 5/1 = 5 10/2=5 15/3=5 20/4=5 25/5=5 30/6=5 Books Price 5 1 10 2 3 15 20 4 5 25 6 30 The constant of proportionality is 5.

  11. Constant of Proportionality Do you remember where the 5 came from? The unit rate…it is the number that you used to multiply by each x value to get each y value. Unit rate is also known as the constant of proportionality because it is the number that remains constant in each proportional situation.

  12. Write the unit rate: Read 80 pages in 2 hours _______ pages in one hour 40

  13. Record your information in the table. dependent independent Which is the dependent variable? Is this a direct proportion? Hours Pages 40 1 Yes…as x increases by the same rate, by y increases by the same rate. 80 2 Which is the independent variable? 3 120 What is the constant of proportionality? k= = 40

  14. Graph It! How do you determine if the graph is a direct proportion? 100 90 80 70 60 50 Pages dependent 40 30 20 10 1 2 3 5 4 Hours A straight line through the origin shows a direct proportion. independent

  15. Write the unit rate: A plane travels 2250 km in 3 hours. What is the average speed? (km per hour) They are asking for unit rate… 750 km/hr What is the constant of proportionality? 750

  16. Graph It! Is this a direct proportion? 2500 2250 2000 1750 1500 dependent Km 1250 1000 750 500 250 Yes…A straight line through the origin shows a direct proportion. 1 2 3 5 4 Hours independent

  17. y x k = y/x Find the first point on the graph and name it using the form (x,y). k = 20/2 (2, 20) k = 10 Plug those into the formula to find the constant of proportionality.

  18. k = 2 Write the equation for the graph above. y = 2x

  19. Write an equation for the information in the table. y = 10x What is the constant of proportionality? 10

  20. k = 5 Write the equation for the graph above. y = 5x

  21. k = 7.5 Write the equation for the graph above. y = 7.5x

  22. Y = 12/x No. The equation is not in the form y = kx.

  23. k = 12.5

  24. Closing How do you find the constant of proportionality from a: Ratio? Table? Equation? Graph? How do you determine if the proportional relationship shown is a direct proportion in a: Table? Graph?

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