Constant of Proportionality - Words
James sends 45 emails in 15 minutes. How many emails did he send per minute?
He sent 3 emails per minute.
This means the constant of proportionality is 3.
Nina earns $12 per hour. Write an equation that represents Nina's earnings. Use y for earnings and x for hours worked.
y=12x
Is this a proportional relationship?
Time (h) Quantity
1 4
2 8
3 14
No.
A runner runs 300 meters in 30 seconds. What unit rate of the relationship between meters and seconds?
10 meters per second.
The unit rate in a proportional relationship
Constant of Proportionality
Liana earned $640 in a 40 hour work week. What is Liana's hourly rate of pay?
Liana earns $16 per hour.
This means the constant of proportionality is 16.
Gianna reads 27 pages in 9 minutes. Write an equation for this relationship using y for the total pages read and x for the number of minutes.
y=3x
Is this a proportional relationship?
Time (h) Quantity (barrels)
1 2.75
2 5.5
3 8.25
Yes, and the constant of proportionality is 2.75.
20 bananas cost 5 dollars. What is the unit rate of the relationship between cost and number of bananas?
$0.25 per banana
two or more ratios that express the same comparison
proportion
A helicopter propeller spins 2400 revolutions in 4 minutes. What is the constant of proportionality.
k = 600
Maxine works at a law office. The equation y = 135x represents her earnings. The variable y is her earnings and x is the number of hours worked.
How much money does she make if she works 40 hours?
$5400
Is this a proportional relationship?
#of tickets cost
2 3
4 6
6 9
Yes. The constant of proportionality is 1.5.
Every 4 hours, a painter paints 2 walls. What is the unit rate of the relationship between walls and hours?
1/2 walls per hour
the relationship between two quantities where one quantity is a constant multiple of the other quantity.
proportional relationship
Jeff earned $400 working a 40-hour work week. How much will Jeff make in 47 hours?
Jeff will make $470 dollars because he makes $10 an hour. k=10
The equation y = 55x represents the rate of the Long Island highway speed limit, in miles per hour. The variable y represents the miles driven and x is the number of hours driven.
How long was Francis driving if he drove 247.5 miles at the speed limit?
4.5 hours
Is this a proportional relationship?
Lbs of Bananas Cost ($)
2 $2.50
3 $3.75
5 $6.25
Yes, and the constant of proportionality is 1.25.
Serena can run 5 1/4 miles in 3/4 of an hour. If she maintains a constant pace, how far can she run in one hour?
What is the name of the two quantities we divide to get the COP in the correct order for division
Output (divided by) Input or
Dependent variable (divided by) Independent variable
Janine sells 16 apples for $8. How much would she earn if she sold 64 apples?
She would earn $24 dollars because she sells at $0.50 per apple. k=0.5
Riding in a taxi costs $2 per mile plus a $10 flat fee. Write an equation that represents this relationship. Let y be the total cost and x be the number of miles.
y=2x+10
Is this a proportional relationship?
Temp (C) Ice Cream Sales
20 2000
25 2500
35 5000
The relationship is NOT proportional.
A rowing team rows 2 1/3 miles in 7/36 of an hour. At this rate, how far can they go in one hour?
12 miles
What is the one ratio present in all proportional relationships?
0:0