Constant of Proportionality - Words
Davion 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.
Jana earns $12 per hour. Write an equation that represents Jana'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
Liam earned $640 in a 40 hour work week. What is Liam's hourly rate of pay?
Liam earns $16 per hour.
This means the constant of proportionality is 16.
Gina 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 ratios that express the same comparison.
equivalent ratios
A helicopter propeller spins 2400 revolutions in 4 minutes. What is the constant of proportionality.
k = 600
Mary 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?
The painter paints 1/2 wall per hour
The relationship between two quantities where one quantity is a constant multiple of the other quantity.
proportional relationship
John earned $400 working a 40-hour work week. How much will Jeff make in 47 hours?
Jeff will make $470 dollars because he makes $10 an hour. k=10
The equation y = 55x represents the rate of the Long Island Highway speed limit, in miles per hour. The variable y represents the miles driven and x is the number of hours driven.
How long was Frank driving if he drove 247.5 miles at the speed limit?
4.5 hours
Is this a proportional relationship?
Lbs of Bananas Cost ($)
2 $2.50
3 $3.75
5 $6.25
Yes, and the constant of proportionality is 1.25.
Every 2.5 hours, a machine produces 2250 basketballs. What is the unit rate of the relationship between basketballs and hours?
900 basketballs per hour
What operation is used to find the constant of proportionality?
division or divide
Janelle sells 16 apples for $8. How much would she earn if she sold 64 apples?
She would earn $32 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.
Every 3.5 hours, a juicer juices 4325 oranges. What is the unit rate of the relationship between oranges and hours?
Round answer to nearest whole number.
Approx 1236 oranges per hour
How can you tell if a given rate is a unit rate?
1 in the denominator