Finding Unit Rates in Proportional Relationships Using Graphs

This lesson teaches how to determine the unit rate of a proportional relationship by examining graphs. It explains the characteristics of proportional relationships, such as a straight line through the origin, and how to identify equivalent rates. The lesson also covers converting rates to unit rates using the multiplicative inverse and provides examples, including calculating unit rates for running speed and piano keys. The importance of understanding unit rates and their application in real-world scenarios is emphasized.

What characteristic of a graph indicates a proportional relationship?

• A line that does not start at the origin

• A straight line through the origin

• A curved line

• A scatterplot with random points

Why is it important that all points on a graph of a proportional relationship have equivalent rates?

• It means the graph is a scatterplot.

• It indicates that the line is curved.

• It shows that the graph is not proportional.

• It allows for the determination of the unit rate from any point.

How do you convert a rate to a unit rate?

• By subtracting the smaller rate from the larger rate

• By dividing the rates by two

• By using the multiplicative inverse

• By adding the rates together

Which of the following is a common misunderstanding about unit rates?

• A simplified rate is always a unit rate.

• Unit rates are not related to multiplicative inverses.

• A unit rate is the same as a proportional rate.

• Unit rates can only be found on curved graphs.

In the example of Dorothy's running speed, what is the unit rate of her running?

• 10 miles per hour

• 8 miles per hour

• 12 miles per hour

• 5 miles per hour

What is the unit rate of white keys per black key on a piano?

• 1 and 2/5 white keys per black key

• 2 white keys per black key

• 3 white keys per black key

• 1 white key per black key

What is the equivalent rate of 35 white keys per 25 black keys when simplified?

• 6 white keys per 4 black keys

• 7 white keys per 5 black keys

• 8 white keys per 6 black keys

• 5 white keys per 3 black keys