Proportional and Nonproportional Relationships

Front

What is a proportional relationship?

Back

A proportional relationship is one in which two quantities increase or decrease at the same rate, meaning the ratio between them remains constant.

Front

What is a non-proportional relationship?

Back

A non-proportional relationship is one where the ratio between two quantities does not remain constant as one quantity changes.

Front

Example of a proportional relationship: If a car travels 60 miles in 1 hour, how far will it travel in 3 hours?

Back

180 miles (60 miles/hour * 3 hours = 180 miles).

Front

Example of a non-proportional relationship: A cell phone plan charges a $25 monthly fee plus $0.05 per text. Is this proportional?

Back

No, it is non-proportional because of the fixed monthly fee.

Front

What does the graph of a proportional relationship look like?

Back

It is a straight line that passes through the origin (0,0).

Front

What does the graph of a non-proportional relationship look like?

Back

It is a straight line that does not pass through the origin.

Front

How can you tell if a table of values represents a proportional relationship?

Back

If the ratios of corresponding values (y/x) are constant, it is proportional.

Front

Does the equation y = 2x + 3 represent a proportional relationship?

Back

No, it does not because of the constant 3 added to 2x.

Front

If a pizza costs $11.99 plus $0.75 for each topping, is this a proportional relationship?

Back

No, it is non-proportional due to the fixed cost of $11.99.

Front

What is the constant of proportionality?

Back

It is the constant ratio (k) in a proportional relationship, represented as y = kx.