Constant of Proportionality
Definition – Constant of Proportionality
Exercise 1
A new self-serve frozen yogurt store opened this summer that sells its yogurt at a price based upon the total weight of the yogurt
and its toppings in a dish. Each member of Isabelle’s family weighed their dish and this is what they found.
Weight (ounces)
Cost ( )
a.
Determine if the relationship is proportional by finding the constant of proportionality.
b.
If x represents the weight and y represents the cost, write an equation that represents the relationship using the constant
of proportionality.
c.
If someone bought 15 ounces worth of yogurt and toppings, how much would they expect to pay? Use your equation from
part (b) to determine the cost.
Exercise 2
Alex spent the summer helping out at his family’s business. He was hoping to earn enough money to buy a new
gaming system
by the end of the summer. Halfway through the summer, after working for weeks, he had earned
. Alex wonders, “If I
continue to work and earn money at this rate, will I have enough money to buy the gaming system by the end of the summer?”
To determine if he will earn enough money, he decided to make a table. He entered his total money earned at the end of Week 1
and his total money earned at the end of Week .
Week (x)
Total Earnings
(y)
a.
Work with a partner to fill in the rest of the chart.
b.
Will Alex be able to earn enough money to buy the gaming system at the end of summer?
c.
Are Alex’s total earnings proportional to the number of weeks he worked? How do you know? (hint: use the constant of
proportionality!)
d.
If x represents the number of weeks and y represents the total money earned, write an equation that represents the
relationship.
Exercise 3
During Jose’s physical education class today, students visited activity stations. Next to each station was a chart depicting how many
calories (on average) would be burned by completing the activity.
Calories Burned while Jumping Rope
x, Time (minutes)
y, Calories Burned
52
a.
Are the calories proportional to the time? Explain how you know.
b.
If x represents the time and y represents the calories burned, can we write an equation that represents the relationship?
Why or why not?
Exercise 4
Kara decides to start a savings account at her local bank. She starts by depositing $50 into her account, then deposits $10 a week
after that. Fill out the following chart showing her total savings.
Week
Total
Savings
a.
Work with a partner to fill in the rest of the chart.
b.
How much money will Kara have saved after 10 weeks? How much money will she have saved after 19 weeks?
c.
Is the amount of money saved proportional to the number of weeks? How do you know?