2. Proportional vs. Non-Proportional 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.

3. Proportional Relationships Will always go through the origin on a graph. (0,0) Graph will always be a straight line.

4. 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 Yes No

5. Let’s Review Guided Practice Graph the proportional relationship “2 pounds of prime rib for $11.” Cost ($) Weight (lb.) Weight(lb. (x) Cost ($) (y) 112 1 5.50 422 Is the weight of the prime rib proportional to the cost?Yes

6. 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? Earnings ($) Hours (h) Unit Rate ( ) 141 282 423 564 Since the simplified ratios were equal, this was a proportional relationship.

7. We typically put time (hours) on the x-axis, and the earnings ($) on the y-axis. Set up the graph paper to fit the data in the chart. You try: Let’s graph this proportional relationship from Ex. 1 on an xy-plane. x y Hours worked Earnings ($) 1 14 28 42 56 2345 Hours (h) Earnings ($) 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.

8. Example 2: 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 Ordered1234 Since all of the simplified ratios are not equal, there is no constant ratio, so this is NOT a proportional relationship.

9. 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 TicketsEarnings ($)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. Now, let’s graph this nonproportional relationship from Ex. 2. 8 12 16 20 28 It passes through the origin, but it is not a straight line.

10. Practice: Graphing Worksheet

11. 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

12. 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