How do you use the constant of proportionality to write an equation that expresses the relationship

between two quantities?

Yards Feet

0 01 32 63 94 12

In this lesson you will learn how to write an equation that expresses the

relationship between two proportional quantities by finding the constant of proportionality.

Let’s Review

y = kx

Let x and y be two proportional quantities.Let k be a constant.

yx

= k xy

= 1k

A Common MistakeAre the quantities proportional?

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5050

100150200

Hours

Mile

s

(0,0)(1,45)

(2,90)(3,135)

(4,180)

451

902

1353

1804

yx

Core Lesson

Write an equation that expresses the relationship between feet and yards.

Yards Feet

0 01 32 63 94 12

Core LessonGraph of feet per yard

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

5

10

15

Yards

Feet

(0,0)(1,3)

(2,6)(3,9)

(4,12)

31

62

93

124

yx

Core LessonRatio of Feet to Yards

31

= 3 62

= 3

93

= 3 124

= 3

Core Lesson

constant of proportionality = 3 feet per yard feet = (3 feet for every yard) x yards

k = feet per yard = 3x = yardsy = feet y = 3 x

In this lesson you have learned how to write an equation that expresses

the relationship between two proportional quantities by finding the constant of proportionality.

Guided PracticeJoe’s cellphone bill was $100 when he talked for 500 mins., $60 when he talked for 300 mins., and $80 when he talked for 400 mins..

Constant of proportionality = Equation:

Extension Activities

Write an equation that relates the cost per gallon of gas, the number of gallons a vehicle’s tank holds, and the total cost to fill the tank. Ask at least 3 adults how much it costs them to fill their gas tank and how much they pay per gallon of gas. Substitute this information into your equation to determine how many gallons of gas their gas tank holds.

Extension Activities

What is your dream job? Research how much people make per year in this profession. Write an equation that relates annual salary, years worked, and total earnings. How many years would you have to work to have earned a million dollars?

Quick Quiz

In January Joe talked on his cellular phone for 500 minutes and his bill was $200. In May he talked for 350 minutes and his bill was $140. Write an equation that relates the minutes, cost per minute, and total bill. What is the constant of proportionality?

Quick QuizA 5 ft. long sidewalk has an area of 35ft2, a 8 ft. long sidewalk has an area of 56 ft2. Write an equation that relates the area, length, and width. What is the constant of proportionality?