How do you identify the constant of proportionality in verbal descriptions of

proportional relationships?

In this lesson you will learn how to identify the constant of proportionality in verbal descriptions of proportional

relationships by writing an equation of the form

y = mx and solving for m.

Let’s Review

y = dependent variablex = independent variable

m = constant of proportionality y = mxm = y x

A Common Mistake

= =x

=

3

12

1

=

Core Lesson

Core Lesson

Core Lesson

distance = rate x time

d = r x t

d = r t

Core Lesson

inches

minutes=

3

12

1

inches

minutes= =x

3

12

1

inches per minute

inches per minute

Core Lesson

distance = rate x time

d = r x t

r = inches per minute

d = t

In this lesson you have learned how to identify the constant of proportionality in verbal descriptions of proportional

relationships by writing an equation of the form

y = mx and solving for m.

Guided Practice

Extension Activities

Research a racing competition of your choice (running, car racing, biking). How long is the race? How much time did it take the top 3

finishers to complete the course? What was each of their constants of proportionality?

Extension Activities

Extension Activities

According to legend the King asked Archimedes if his crown was made from pure

gold or if it had some silver in it. Archimedes figured out that the volume of

the crown is 125 cm3 and that the mass was 1.8 kgs. He also knows that 1 kg of gold has a volume of 50 cm3 and 1 kg of silver has a

volume of 100 cm3. Is the crown pure gold? If not, how much silver is in it. Explain your

reasoning and show all of your work.

Quick Quiz

A car travels 187.5 miles in 2 hours and 30 minutes and 337.5 miles in 4 hours and 30

minutes. What is the constant of proportionality?

A bicyclist travels 67.5 miles in 2 hours and 30 minutes and 121.5 miles in 4 hours and 30

minutes. What is the constant of proportionality?