Exploring Proportional Relationships Through Multiple Representations

The video tutorial explores multiple representations of proportional relationships. It begins with an introduction to the concept, followed by two examples. The first example involves a dolphin traveling at a constant speed of 40 miles per hour, demonstrating how to represent this scenario using a table, equation, and graph. The second example focuses on Sarah's earnings from working at an ice cream shop, showing how to determine the constant of proportionality and represent it in various forms. The tutorial emphasizes understanding and applying these concepts through practical examples.

What is the rate at which a dolphin travels through water?

• 40 miles per hour

• 60 miles per hour

• 20 miles per hour

• 80 miles per hour

How far does the dolphin travel after 3 hours?

• 120 miles

• 200 miles

• 160 miles

• 80 miles

What represents the constant of variation in the dolphin's travel?

• 20

• 80

• 60

• 40

How is the graph's y-axis labeled for the dolphin's travel?

• Miles traveled

• Hours traveled

• Speed in mph

• Time in seconds

What is Sarah's hourly wage at the ice cream shop?

• $6 per hour

• $8 per hour

• $12 per hour

• $10 per hour

How much does Sarah earn after working 4 hours?

• $32

• $24

• $40

• $16

What is the constant of proportionality for Sarah's earnings?

• 12

• 6

• 10

• 8

How is the x-axis labeled on the graph for Sarah's earnings?

• Dollars earned

• Hours worked

• Days worked

• Number of ice creams sold

What does the ordered pair (2, 16) represent in Sarah's earnings graph?

• 2 days worked and $16 earned

• 16 hours worked and $2 earned

• 16 ice creams sold in 2 hours

• 2 hours worked and $16 earned

What is the method used to find the constant of proportionality in both examples?

• Subtracting y from x

• Adding x and y

• Multiplying x by y

• Dividing y by x