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
A runner runs 300 meters in 30 seconds. What unit rate of the relationship between meters and seconds?
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
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
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.
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
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.
Every 3.5 hours, a juicer juices 4325 oranges. What is the unit rate of the relationship between oranges and hours?
Approx 1235 oranges per hour