Proportional vs Non-Proportional Relationships

Front

What is a proportional relationship?

Back

A proportional relationship is one in which two quantities maintain a constant ratio or rate. For example, if y is directly proportional to x, then y = kx, where k is a constant.

Tags

CCSS.7.RP.A.2A

Front

What is a non-proportional relationship?

Back

A non-proportional relationship is one where the ratio between two quantities is not constant. This often involves an additional constant term, such as in the equation y = mx + b, where b is not zero.

Tags

CCSS.7.RP.A.2D

Front

What does the slope (m) represent in the equation y = mx + b?

Back

The slope (m) represents the rate of change of y with respect to x. It indicates how much y changes for a unit change in x.

Tags

CCSS.8.EE.B.5

Front

What does the y-intercept (b) represent in the equation y = mx + b?

Back

The y-intercept (b) represents the value of y when x is zero. It is the point where the line crosses the y-axis.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How can you identify a proportional relationship from a graph?

Back

A proportional relationship can be identified from a graph if the line passes through the origin (0,0) and is straight.

Tags

CCSS.7.RP.A.2D

Front

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

Back

A non-proportional relationship can be identified from a graph if the line does not pass through the origin or if it is not straight.

Tags

CCSS.7.RP.A.2D

Front

What is a unit rate?

Back

A unit rate is a comparison of two different quantities when they are combined together. It is expressed as a quantity per one unit of another quantity.

Tags

CCSS.6.RP.A.1

CCSS.6.RP.A.2

Front

Give an example of a proportional relationship in real life.

Back

An example of a proportional relationship is the cost of apples if they are sold at a constant price per pound. If apples cost $2 per pound, then 3 pounds cost $6, maintaining a constant ratio.

Tags

CCSS.7.RP.A.2A

Front

Give an example of a non-proportional relationship in real life.

Back

An example of a non-proportional relationship is a taxi fare that includes a base fee plus a charge per mile. The total fare does not maintain a constant ratio to the distance traveled.

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