How do you identify the constant of proportionality from labeled diagrams?

1. 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

2. In this lesson you will learn how to identify the constant of proportionality from a labeled diagramby writing an equation of the form y=mx and solving for m.

3. Constant of Proportionality – the constant value of the ratio of two proportional quantities x and y. y = mx y x 1 = m = x y m

5. 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.

6. Joe’s Wafers Cellphone Computer Television C 3.14 nm d = 1 nm C 31.4 nm d = 10 nm C 314 nm d = 100 nm

7. c = circumference = dependent variable d = diameter = independent variable = constant of proportionality

8. Joe’s Wafers Cellphone Computer Television C 314 nm d = 100 nm C 31.4 nm d = 10 nm C 3.14 nm d = 1 nm 31.4 314 3.14 10 100 1

9. 3.14 3.14 = = 1 31.4 3.14 = = 10 314 3.14 = = 100

10. c = circumference = dependent variable d = diameter = independent variable = constant of proportionality

11. In this lesson you have learned how to identify the constant of proportionality from a labeled diagramby writing an equation of the form y = mx and solving for m.

12. What is the constant of proportionality? 0 2 4 6 8 10

13. Create a scale map of your classroom. What is the constant of proportionality in this situation?

14. 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?

15. 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?