Exploring Proportional Relationships and Graphs

This video tutorial covers the concept of proportional relationships and how to identify them using graphs. It explains the criteria for a relationship to be proportional, such as passing through the origin and forming a straight line. Two examples are provided: one involving internet cafe charges, which is non-proportional, and another involving shower head water usage, which is proportional. The video guides students through graphing these examples and analyzing their proportionality. It concludes with a recap and encouragement for students to apply these concepts in their exercises.

What is the format of a proportional relationship?

• y = a/x

• y = a + x

• y = ax

• y = ax + b

How can you tell if a relationship is proportional by looking at a graph?

• If it is a straight line that passes through the origin

• If it is a straight line that does not pass through the origin

• If it is a curved line

• If it is a horizontal line

What is the service fee charged by the internet cafe in Example 1?

• $9

• $7

• $5

• $2

What is the total cost for 2 hours of internet usage in Example 1?

• $7

• $11

• $9

• $13

Why is the relationship in Example 1 not proportional?

• The graph does not pass through the origin

• The service fee is too high

• The cost per hour is not constant

• The graph is not a straight line

What is the water usage per minute for shower heads manufactured before 1994?

• 6 gallons

• 5 gallons

• 4 gallons

• 3 gallons

How many gallons of water are used in 3 minutes according to Example 2?

• 25 gallons

• 20 gallons

• 15 gallons

• 10 gallons

What is the constant of proportionality in Example 2?

• 5

• 6

• 4

• 3

Why is the relationship in Example 2 considered proportional?

• The graph is a straight line that passes through the origin

• The graph is a curved line

• The graph does not pass through the origin

• The water usage per minute is not constant

What should you use to ensure your graph lines are straight?

• A pencil

• A ruler

• A compass

• A marker