### Constant of Proportionality

```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?
```