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 ratios that express the same comparison
equivalent ratios
A helicopter propeller spins 2500 revolutions in 4 minutes. What is the constant of proportionality for revolutions per minute.
k = 626.25
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 if he earns an extra $2 per hour for anything over 40 hours?
Jeff will make $484 dollars because he makes $10 an hour for the first 40 hours. Then he earns $12 per hours the last 7 hours he worked.
The equation y = 55x represents the rate of the Long Island highway speed limit, in miles per hour. The variable y represents the miles driven and x is the number of hours driven.
How long was Francis driving if he drove 247.5 miles at the speed limit?
4.5 hours
Is this a proportional relationship?
Lbs of Bananas Cost ($)
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
What operation is used to find the constant of proportionality?
division or divide y/x
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. (Hint: it is not going to be proportional)
y=2x+10
Is this a proportional relationship?
Temp (C) Ice Cream Sales
20 2000
25 2500
50 5000
60 5500
The relationship is NOT proportional because the last row did not have the same C.O.P.
Every 3.5 hours, a juicer juices 4305 oranges. What number of oranges could be juiced in 1 minute?
Approx 20.5 oranges per minute
This is the format that all proportional equations are in.
what is y=k(x)