2.  A constant ratio in any proportional relationship  Really just another name for unit rate! Remember, to be constant means it never changes!

3. Miles 50100150200 Gallons 2468 Find the unit rate! 25 miles per gallon This means our constant of proportionality is 25, so if we divide the miles by gallons we should always get 25. Let’s check! Find the constant of proportionality/variation/slope between the gallons and the miles.

4. Number of Apples 92736 Cost $3.00$9.00$12.00 Find the constant of proportionality/variation/slope between gallons and miles. Find the unit rate! Constant of proportionality = 3 Let’s Check!

5. (0,0) (1,45) (2,90) (3,135) (4,180) Y4590135180 X1234 Find the constant of proportionality. To find our constant of proportionality we have to divide! 45 1 = 90 2 =45 135 3 =45 180 4 =45 So, our constant of proportionality is 45. We could write this as: y=45(x)

6. We will ALWAYS be able to write our constant of proportionality as an equation that looks like this: y=kx In our last example we had: y = 45x And “k” will always be our constant of proportionality/variation/slope! Unit Rate Constant of Proportionality Constant of Variation Slope

7. U-Swirl Frozen Yogurt Weight (oz)Cost 9$2.25 11$2.75 13$3.25 Weight (oz)Cost

8. MineCraft MinutesBlocks 580 12192 35560 Minutes Blocks

9. Baking MinutesCookies 1012 2024 3039 There is no constant of proportionality because there isn’t a constant rate!

10. Weight (lb.) Cost ($) Weight (lb.) 24 6 81012 6 18 24 30 36 42

11. Gallons Cost ($) Gallons of Gas 24 6 81012 6 18 24 30 36 42

12. Cost ($) Gallons of Gas 24 6 81012 6 18 24 30 36 42 There is no constant of proportionality because there isn’t a constant rate!

13.  If two quantities are proportional, then they have a constant ratio.  To have a constant ratio means two quantities have the same unit rate.  If the ratio is not constant, the two quantities are said to be non-proportional.  So, the two quantities do not have the same unit rate.

14.  Will always go through the origin on a graph. (0,0)  Graph will always be a straight line.

15. In order to tell if a graph is proportional the line must go through the origin. Tell if the following graphs represent a proportional relationships. Proportional ? _________ Why? Line goes through the origin Why? Line does not go through the origin YesNo

16. Let’s Review Guided Practice State in words the proportional relationship shown here. (There are many correct answers!) Distance (ft.) Time (min.) 2 feet per min

17. Let’s Review Quick Quiz State in words the proportional relationship shown here. (There are many correct answers!) Cost ($) Weight (ounces) You Try 5oz for $2

18. You try: The following chart shows how much money Alex earns for mowing lawns. Is the amount of money he earns proportional to the number of hours that he spends mowing? Earnin gs ($) Hours (h) Unit Rate ( ) 141 282 423 564 Since the simplified ratios were equal, this was a proportional relationship.

19. We typically put time (hours) on the x-axis, and the earnings ($) on the y-axis. Set up the graph paper to fit the data in the chart. x y Hours worked Earnings ($) 1 14 28 42 56 2345 Hour s (h) Earnin gs ($) Point (x, y) 114(1, 14) 228(2, 28) 342(3, 42) 456(4, 56) Plot points (x, y) from the table. Connect the points. Describe the graph of this proportional relationship.

20. Ticket Express charges $7 per movie ticket plus a $3 processing fee per order. Is the cost of an order proportional to the number of tickets ordered? Explain. Cost ($)10172431 Tickets Ordered 1234 Since all of the simplified ratios are not equal, there is no constant ratio, so this is NOT a proportional relationship.

21. Tickets ordered will be on the x-axis, and the cost ($) will be on the y-axis. x y Tickets ordered Cost ($) 1 4 24 32 23 4 Tickets Earnings ($) Point (x, y) 00(0,0) 110(1, 10) 217(2, 17) 324(3, 24) 431(4, 31) Plot points (x, y) from the table. Connect the points. Describe the graph of this nonproportional relationship. 8 12 16 20 28 It passes through the origin, but it is not a straight line.