Exploring Proportional Relationships

The video tutorial explains how to compare proportional relationships using tables, graphs, and equations. It demonstrates finding the constant of proportionality, which is the slope or unit rate, for different scenarios. The example involves three individuals, Luke, Michael, and Alexander, who run laps to prepare for basketball season. Their performances are analyzed using different mathematical representations, and their running rates are compared to determine who is the fastest.

What is the purpose of comparing proportional relationships?

• To find the fastest runner

• To understand different representations of data

• To calculate the area of a graph

• To memorize equations

Why is it preferable to use whole numbers when finding the constant of proportionality?

• Decimals are not allowed in mathematics

• It makes the graph look better

• Whole numbers are required by law

• It simplifies calculations

What does a constant of proportionality of 2 over 1 signify?

• 1 lap per 2 minutes

• 2 laps per 2 minutes

• 1 lap per minute

• 2 laps per minute

What does a constant of proportionality of 5 over 1 indicate?

• 1 lap per 5 minutes

• 5 laps per 2 minutes

• 2 laps per minute

• 5 laps per minute

Why do we need to keep the ratio of x and y the same throughout the analysis?

• To maintain consistency

• Because it's easier to remember

• To make the graph look uniform

• To comply with mathematical standards

Why is it important to verify the proportionality in a table by checking multiple values?

• To practice arithmetic

• To make the table look complete

• Because it's a mathematical rule

• To ensure accuracy

How is the constant of proportionality related to the slope of a line?

• It is the inverse of the slope

• It is the y-intercept

• They are unrelated

• It is the same as the slope

What adjustment is made to Alexander's constant of proportionality to write it as a unit rate?

• Multiply by 2

• Subtract 1

• Divide by 2

• Add 1

Who was the fastest runner according to the constant of proportionality?

• Alexander

• Michael

• Luke

• They all ran at the same speed

What is the unit rate of Alexander's constant of proportionality after adjustment?

• 0.5 laps per minute

• 1.5 laps per minute

• 1 lap per minute

• 2 laps per minute