11.08 Multiple Representations of Proportional Relationships

Front

What is the unit rate/constant of proportionality?

Back

The unit rate or constant of proportionality is the ratio of two quantities that describes how one quantity changes in relation to another. For example, if a car travels 40 miles in 1 hour, the unit rate is 40 miles per hour.

Front

What does it mean if a relationship is proportional?

Back

A relationship is proportional if two quantities maintain a constant ratio or rate. This means that as one quantity increases or decreases, the other quantity does so in a consistent manner.

Front

How can you determine if a table shows a proportional relationship?

Back

To determine if a table shows a proportional relationship, check if the ratios of the corresponding values are constant. If they are, the relationship is proportional.

Front

What is an example of a proportional relationship in real life?

Back

An example of a proportional relationship is the cost of apples. If 1 pound costs $2, then 2 pounds cost $4, 3 pounds cost $6, and so on. The cost per pound remains constant.

Front

What is the formula for finding the unit rate?

Back

The formula for finding the unit rate is: Unit Rate = Total Quantity / Number of Units. For example, if you travel 120 miles in 3 hours, the unit rate is 120 miles / 3 hours = 40 miles per hour.

Front

What does a graph of a proportional relationship look like?

Back

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

Front

If Evan bought 5 pounds of bananas for $10, what is the cost per pound?

Back

The cost per pound is $10 / 5 pounds = $2 per pound.

Front

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

Back

Proportional relationships have a constant ratio between two quantities, while non-proportional relationships do not maintain a constant ratio.

Front

How can you represent a proportional relationship using an equation?

Back

A proportional relationship can be represented by the equation y = kx, where k is the constant of proportionality.

Front

What does it mean if a graph does not pass through the origin?

Back

If a graph does not pass through the origin, it indicates that the relationship is not proportional, as there is no constant ratio between the two quantities.