Comparing Proportional and Nonproportional Relationships

This video tutorial focuses on comparing proportional and non-proportional relationships. It uses examples from two smoothie shops to illustrate these concepts. Smoothie Shop A demonstrates a proportional relationship with a constant price per ounce, while Smoothie Shop B shows a non-proportional relationship with varying prices. The video explains that in a proportional relationship, the quotient of two quantities remains constant. It introduces the concept of the constant of proportionality and provides equations to represent these relationships. The video concludes by summarizing the key points discussed.

What is the main focus of this video?

• Exploring geometric shapes

• Learning about quadratic functions

• Comparing proportional and non-proportional relationships

• Understanding linear equations

Tags

CCSS.8.EE.B.5

In smoothie shop A, what is the cost per ounce of a smoothie?

• 1.25 dollars

• 1 dollar

• 50 cents

• 75 cents

Tags

CCSS.6.RP.A.1

CCSS.6.RP.A.2

Which equation represents the relationship between size and price in smoothie shop A?

• p = 0.5s

• p = 0.75s

• p = s + 0.75

• p = 1.25s

Tags

CCSS.7.RP.A.2C

Why is the relationship in smoothie shop B not proportional?

• The sizes are not listed

• The prices are not in dollars

• The cost per ounce is different for each size

• The cost per ounce is the same for each size

Tags

CCSS.7.RP.A.2A

What is a key characteristic of quantities in a proportional relationship?

• They have different quotients

• They have the same quotient

• They are always integers

• They are always positive

Tags

CCSS.7.RP.A.2A

In a table of values for two related quantities, what indicates a proportional relationship?

• Random values

• Same quotient for each pair

• Negative values

• Different quotients for each pair

Tags

CCSS.7.RP.A.2A

What is the constant of proportionality often referred to as?

• c

• k

• b

• m

Tags

CCSS.7.RP.A.2B

Which equation represents a proportional relationship?

• y = k/x

• y = kx

• y = x + k

• y = k - x

Tags

CCSS.7.RP.A.2C

If y is proportional to x, what will y/x always equal?

• x

• k

• 1

• 0

Tags

CCSS.7.RP.A.2B

What does it mean if an equation cannot be written in the form y = kx?

• It is a linear equation

• It is a quadratic equation

• It does not represent a proportional relationship

• It represents a proportional relationship

Tags

CCSS.7.RP.A.2C