Proportional Relationships and Equations

The lesson covers proportional relationships, focusing on writing two equations for each relationship by identifying two constants of proportionality. Examples include mixing paint, baking, and travel scenarios. The lesson emphasizes that constants of proportionality are reciprocals when variables are switched, allowing for different equations to represent the same relationship.

What is the main focus of the lesson on proportional relationships?

• Exploring different types of graphs

• Understanding the concept of ratios

• Learning to write two equations for each relationship

• Studying the history of mathematics

In the paint mixing example, what is the constant of proportionality when red paint is the variable?

• 8

• 2

• 1

• 4

What is the equation for blue paint in terms of red paint in the paint mixing example?

• b = 5r

• b = 3r

• b = 2r

• b = 4r

In the baking example, what is the unit rate for cups of flour per tablespoon of honey?

• 2/3

• 3/2

• 4/5

• 5/4

What is the equation for flour in terms of honey in the baking example?

• f = 4/5 h

• f = 5/4 h

• f = 2/3 h

• f = 3/2 h

In the travel example, what is the speed in miles per hour?

• 810

• 710

• 610

• 510

What is the equation for distance in terms of time in the travel example?

• d = 510t

• d = 610t

• d = 710t

• d = 810t

What is the reciprocal of the constant of proportionality 5/4?

• 5/3

• 4/5

• 3/5

• 2/3

What is the key takeaway about constants of proportionality when switching variables?

• They become zero

• They are reciprocal numbers

• They remain the same

• They double in value

What is the purpose of writing two equations for a proportional relationship?

• To ensure accuracy

• To make calculations easier

• To provide multiple perspectives

• To confuse the students