How do you identify the constant of proportionality in verbal descriptions of proportional relationships?

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Presentation transcript:

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 variable x = independent variable m = constant of proportionality y = mx m = y x

A Common Mistake ==x = =

Core Lesson

distance = rate x time d = r x t d = r t

inches minutes = inches minutes ==x 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?

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 cm 3 and that the mass was 1.8 kgs. He also knows that 1 kg of gold has a volume of 50 cm 3 and 1 kg of silver has a volume of 100 cm 3. 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 miles in 2 hours and 30 minutes and 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 miles in 4 hours and 30 minutes. What is the constant of proportionality?