Proportional Relationships

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Proportional Relationships

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Presentation transcript:

Proportional Relationships 1/18/2019 Identifying Proportional Relationships From graphs 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.

Since the simplified ratios were equal, 1/18/2019 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 ( ) 14 1 28 2 42 3 56 4 Since the simplified ratios were equal, this was a proportional relationship.

Let’s graph this proportional relationship from Ex. 1 on an xy-plane. We typically put time (hours) on the x-axis, and the earnings ($) on the y-axis. Set up the graph paper to fit the data in the chart. Plot points (x, y) from the table. y Hours (h) Earnings ($) Point (x, y) 1 14 (1, 14) 2 28 (2, 28) 3 42 (3, 42) 4 56 (4, 56) 56 42 Earnings ($) 28 14 Connect the points. x 1 2 3 4 5 Describe the graph of this proportional relationship. Hours worked

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

between cost and the number of tickets ordered. Example 2: Ticket Express charges $7 per movie ticket plus a $3 processing fee per order. Is the cost of an order proportional to the number of tickets ordered? Explain . Cost ($) 10 17 24 31 Tickets Ordered 1 2 3 4 Since all of the simplified ratios are not equal, there is NOT a proportional relationship between cost and the number of tickets ordered.

Now, let’s graph this nonproportional relationship from Ex. 2. Tickets ordered will be on the x-axis, and the cost ($) will be on the y-axis. y Plot points (x, y) from the table. 32 Tickets Earnings ($) Point (x, y) 1 10 (1, 10) 2 17 (2, 17) 3 24 (3, 24) 4 31 (4, 31) 28 24 Cost ($) 20 16 12 8 4 Connect the points. x Describe the graph of this nonproportional relationship. 1 2 3 4 Tickets ordered

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