Understanding Proportional Relationships

The video tutorial explains proportional relationships, where one variable is a constant multiple of another. It provides examples, such as distance traveled at a constant speed and total mass of identical bricks, to illustrate proportional and non-proportional situations. The tutorial also demonstrates how to test proportionality using tables, focusing on the ratio of variables. It concludes with an analysis of paddle board rental costs to identify proportional relationships.

What defines a proportional relationship between two variables X and Y?

• Y is equal to X squared

• Y is equal to a constant divided by X

• Y is equal to X plus a constant

• Y is equal to a constant times X

Which of the following scenarios represents a proportional relationship?

• The cost of concert tickets with a service charge

• The height of a plant over time with varying growth rates

• The distance a train travels at a constant speed

• The total cost of groceries with a discount

Why is the cost of concert tickets with a service charge not proportional?

• The number of tickets varies

• The service charge is a percentage

• The service charge is a constant addition

• The price per ticket changes

In the context of bricks, what makes the relationship proportional?

• Each brick has a different weight

• The total mass is a constant times the number of bricks

• The weight of bricks changes over time

• The number of bricks is fixed

What is the key indicator of a proportional relationship in a table of values?

• The sum of Y values is constant

• The ratio of Y to X is constant

• The difference between Y and X is constant

• The product of Y and X is constant

In the first table example, why is the relationship not proportional?

• The sum of X and Y is constant

• The values of Y are not decreasing

• The values of X are not increasing

• The ratio of Y to X is not constant

Which table represents a proportional relationship?

• The table where Y divided by X equals 14, 10, and 7

• The table where Y divided by X equals 7 consistently

• The table where Y divided by X equals 15, 10, and 7

• The table where Y divided by X equals 20, 15, and 10

What is the ratio of Y to X in the proportional table?

• 14

• 10

• 7

• 5

In the final example, which business has a proportional cost structure?

• Water Waves

• Lake Rentals

• Paddle Pro

• Board Buddies

What is the significance of a constant ratio in determining proportionality?

• It implies a non-linear relationship

• It suggests a variable relationship

• It shows a quadratic relationship

• It indicates a linear relationship