1. Today, we will graph the information from the tables of values that we worked with yesterday in class. Our objective is to use a graph to identify if a relationship is proportional or not.

2. Example 1: 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.

3. We typically put time (hours) on the x-axis, and the earnings ($) on the y-axis. Set up the graph paper to fit the data in the chart. Let’s graph this proportional relationship from Ex. 1 on an xy-plane. x y Hours worked Earnings ($) 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.

4. The graph of a proportional relationship: is a straight line, AND it passes through the origin, or point (0,0).

5. 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 NOT a proportional relationship between cost and the number of tickets ordered.

6. 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 Ticket s Earnings ($) Point (x, y) 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

7. This graph shows a nonproportional relationship. It is a straight line, but it does not pass through the origin.

8. Example 3: Isaiah is selling candy bars to help raise money for his scouting troop. Isaiah sold two candy bars for $3. Complete the rest of the chart based on that information and find the unit rate for each. Chocolate Bars Sold(x) Money Received (y) Unit Rate ( ) 2$3 4$6 6$9 8$12

9. We typically put earnings ($) on the y-axis. Set up the graph paper to fit the data in the chart. Let’s graph this non-proportional relationship from Ex. 1 on an xy- plane. x y Chocolate Bars Sold Money Earned($) Chocolate bars (x) Money (y) Point (x, y) 23(2, 3) 46(4, 6) 69(6, 9) 812(8, 12) Plot points (x, y) from the table. Connect the points. Describe the graph of this proportional relationship. Chocolate Bars Sold 12 2 4 6 8 10 2468 12

10. This graph shows a proportional relationship. It is a straight line, and it does not pass through the origin.