Proportional vs. Nonproportional Relationoships

Front

What is a proportional relationship?

Back

A proportional relationship is a relationship between two quantities where the ratio of one quantity to the other is constant. This means that as one quantity increases or decreases, the other quantity does so in a consistent manner.

Tags

CCSS.7.RP.A.2A

Front

What is a non-proportional relationship?

Back

A non-proportional relationship is a relationship between two quantities where the ratio is not constant. This often involves a fixed amount added or subtracted, leading to a change in the ratio.

Tags

CCSS.7.RP.A.2D

Front

How can you identify a proportional relationship from a graph?

Back

A graph represents a proportional relationship if it is a straight line that passes through the origin (0,0).

Tags

CCSS.7.RP.A.2D

Front

How can you identify a non-proportional relationship from a graph?

Back

A graph represents a non-proportional relationship if it is a straight line that does not pass through the origin or if it is not a straight line.

Tags

CCSS.7.RP.A.2D

Front

What does it mean if a relationship is described as 'directly proportional'?

Back

A directly proportional relationship means that as one quantity increases, the other quantity increases at a constant rate, maintaining a constant ratio.

Tags

CCSS.7.RP.A.2D

Front

What does it mean if a relationship is described as 'indirectly proportional'?

Back

An indirectly proportional relationship means that as one quantity increases, the other quantity decreases, and vice versa, maintaining a constant product.

Tags

CCSS.7.RP.A.2A

Front

Example of a proportional relationship: If 1 bag of popcorn costs $2.50, how much do 4 bags cost?

Back

4 bags cost $10.00 (2.50 x 4 = 10.00).

Tags

CCSS.7.RP.A.2A

Front

Example of a non-proportional relationship: If a video game rental costs $15 plus $3 per day, what is the cost for 2 days?

Back

The cost for 2 days is $21 ($15 + $3*2 = 21).

Tags

CCSS.7.RP.A.2D

Front

What is the significance of the origin in determining proportional relationships?

Back

The origin (0,0) is significant because if a graph passes through it, it indicates that when one quantity is zero, the other is also zero, which is a characteristic of proportional relationships.

Tags

CCSS.7.RP.A.2D

Front

If a table shows values that double consistently, what type of relationship does it represent?

Back

It represents a proportional relationship.

Tags

CCSS.7.RP.A.2A