Proportional vs. NonProportional Relationships

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What is a proportional relationship?

Back

A proportional relationship is a relationship between two variables where their ratio is constant. This means that as one variable changes, the other variable changes at a consistent rate.

Tags

CCSS.7.RP.A.2D

Front

What is a non-proportional relationship?

Back

A non-proportional relationship is a relationship between two variables where the ratio is not constant. This means that the change in one variable does not consistently correspond to a change in the other variable.

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What does the constant of proportionality (k) represent?

Back

The constant of proportionality (k) represents the ratio between two proportional quantities. It is the factor by which one variable is multiplied to obtain the other.

Tags

CCSS.7.RP.A.2B

Front

How can you identify a proportional relationship from a table?

Back

A table represents a proportional relationship if the ratios of the corresponding values are constant. For example, if the ratio of y to x is the same for all pairs, the relationship is proportional.

Tags

CCSS.7.RP.A.2D

Front

What does a proportional relationship look like on a graph?

Back

A proportional relationship on a graph is represented by a straight line that passes through the origin (0,0). The slope of the line represents the constant of proportionality.

Tags

CCSS.7.RP.A.2D

Front

What is the equation for a proportional relationship?

Back

The equation for a proportional relationship is y = kx, where k is the constant of proportionality.

Tags

CCSS.7.RP.A.2C

Front

What is the difference between proportional and non-proportional graphs?

Back

Proportional graphs are straight lines that pass through the origin, while non-proportional graphs do not pass through the origin and may curve or have different slopes.

Tags

CCSS.7.RP.A.2D

Front

If Shawn makes $7.50 an hour, how can this relationship be described?

Back

This relationship is proportional because the amount earned is directly related to the number of hours worked, maintaining a constant rate of $7.50 per hour.

Tags

CCSS.7.RP.A.2A

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What is an example of a non-proportional relationship?

Back

An example of a non-proportional relationship is the cost of a phone plan that has a fixed monthly fee plus a charge per minute. The total cost does not have a constant ratio to the number of minutes used.

Tags

CCSS.7.RP.A.2D

Front

How do you determine if a table is non-proportional?

Back

A table is non-proportional if the ratios of the corresponding values are not constant. If you find different ratios for different pairs, the relationship is non-proportional.

Tags

CCSS.7.RP.A.2A