1. + Directly Proportional

2. + Directly proportional: as one amount increases, another amount increases at the same rate. Hence, the straight line when we graph information

3. + Directly Proportional Example: you are paid $20 an hour How much you earn is directly proportional to how many hours you work Work more hours, get more pay; in direct proportion. This could be written: Earnings directly proportional to hours worked If you work 2 hours you get paid $40 If you work 3 hours you get paid $60

4. + Directly Proportional The "constant of proportionality" is the value that relates the two amounts Example: you are paid $20 an hour The constant of proportionality is 20 because: Earnings = 20 × Hours worked

5. + Direct and Constant Proportionality This can be written: y = kx Where k is the constant of proportionality

6. + Example: y is directly proportional to x, and when x=3 then y=15. What is the constant of proportionality? They are directly proportional, so: y = kx Put in what we know (y=15 and x=3): 15 = k × 3 Solve (by dividing both sides by 3): 15/3 = k × 3/3 5 = k × 1 k = 5 The constant of proportionality is 5: y = 5x

7. + Determine the constant of proportionality for each table Express your answer as y = kx y = 10x

8. + Determine the constant of proportionality for each table

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14. + Determine the Constant of Proportionality for each graph Identify the constant of proportionality. Write your answer as y = kx Determine what you multiply by at each point (relationship between x ad y)

15. + Determine the Constant of Proportionality for each graph Relationship between each point it to multiply by 3

16. + Determine the Constant of Proportionality for each graph Relationship between each point it to multiply by 5

17. + Determine the Constant of Proportionality for each graph Relationship between each point it to multiply by 6