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How do you identify the constant of proportionality from labeled diagrams? » C 3.14 nm d = 1 nm » C 31.4 nm d = 10 nm » C 314 nm d = 100 nm In this lesson you will learn how to identify the constant of proportionality from a labeled diagram by writing an equation of the form y=mx and solving for m. Let’s Review Constant of Proportionality – the constant value of the ratio of two proportional quantities x and y. y = mx y x = m x y = 1 m A Common Mistake Core Lesson Joe is a nanotechnologist who makes circular wafers for electronic devices. Given the information in the diagram write an equation of the form y = mx and solve for m. Core Lesson Joe’s Wafers Cellphone Computer » C 3.14 nm d = 1 nm » C 31.4 nm d = 10 nm Television » C 314 nm d = 100 nm Core Lesson c = circumference = dependent variable d = diameter = independent variable = constant of proportionality Core Lesson Joe’s Wafers Cellphone Computer » C 3.14 nm d = 1 nm Television » C 31.4 nm d = 10 nm » C 314 nm d = 100 nm 3.14 31.4 314 1 10 100 Core Lesson 3.14 = 3.14 = = 3.14 = = 3.14 = 1 31.4 10 314 100 Core Lesson c = circumference = dependent variable d = diameter = independent variable = constant of proportionality In this lesson you have learned how to identify the constant of proportionality from a labeled diagram by writing an equation of the form y = mx and solving for m. Guided Practice 0 What is the constant of proportionality? Color Weight Distance Green 50 g 2 cm Orange 100 g 4 cm Yellow 150 g 6 cm Blue 200 g 8 cm 2 4 6 8 10 Extension Activities Create a scale map of your classroom. What is the constant of proportionality in this situation? Extension Activities Fill a beaker with 50 ml of water. What is the mass of the water? What is the density of water? Fill a beaker with 50 ml of corn syrup. What is the mass of the corn syrup? What is the density of corn syrup? Fill a beaker with 50 ml of oil. What is the mass of the oil? What is the density of oil? Finally, combine the oil, water, and corn syrup. What happens and why? Quick Quiz Write an equation that relates the perimeter of a square and the length of each side of the square. What is the constant of proportionality? Write an equation that relates the perimeter of an equilateral triangle and the length of each side of the equilateral triangle. What is the constant of proportionality?