Constant of Proportionality in Words
Constant of Proportionality in Equations
Tables and Graphs
Unit Rate
Comparing Proportional Relationships
100
Jude sends 45 E-mails in 15 minutes.
How many E-mails did he send per minute?
He sent 3 E-mails per minute.
100
Navelle earns $12 per hour. Write an equation that represents Navelle's earnings.
y = 12x
100
Does this table show a proportional relationship? Explain how you know.
The relationship is proportional because if we divide each cost per number of tickets, we see the constant of proportionality is $1.50 per ticket.
100
Every 2.5 hours, a machine produces
2250 basketballs. How many basketballs can the machine produce in 1 hour? Write and Solve the unit rate.
900 basketballs per hour
100
Kelsea earns $540 in 36 hours of working.
Brittany earns $320 for 28 hours of working.
Sarah earns $580 for 39 hours of working.
Who earns the most money?
Kelsea: $15.00 per hour
Brittany: $11.43 per hour
Sarah: $14.87 per hour
Kelsea earns more money
200
Lenasia earned $640 in a 40-hour work week.
What is Lenasia's hourly rate of pay?
Lenasia earns $16 per hour.
200
Gianna reads 27 pages in 9 minutes. At What rate does Gianna read?
Write an equation for this relationship.
Gianna reads 3 pages per minute.
y = 3x
200
Does this table represent a proportional relationship? Explain how you know.
The table does not represent a proportional relationship because when we divide the sales of ice cream by each temperature, we do not get a constant value.
200
Beverly earns $300 for working 2 weeks. How much would she earn if she worked 9 weeks? Write and solve this unit rate.
$/weeks
300/2 = ?/9
$1,350 in 9 weeks
200
What is the constant of proportionality?
y = 7x
k=7
300
A helicopter propeller spins 2400 revolutions in 4 minutes. What is the constant of proportionality (k), in revolutions per minute?
The constant of proportionality is k = 600 RPM.
300
Maxine works at law office. the equation y = 135x represents her earnings. Determine how much money she makes if she works 40 hours.
Maxine earns $5,400 in 40 hours.
300
A graph represents a proportional relationship if:
1.
2.
1. It is a straight line
2. It passes through the origin
300
A rental company charges $80 per day. How much money would you spend if you rented the car for 12 days? Write and solve the unit rate.
$/days
80/1 = ?/12
$960 for 12 days
300
Which has the greater constant of proportionality? Explain.
y = 4.2x
4 pounds of walnuts costs $18.
4.5 is greater than 4.2.
400
Jeff earned $400 working a 40-hour work week.
Find Jeff's hourly wage and use it to predict how much he will make if he works for 47 hours.
Jeff makes $10 per hour and would make $470 IN 47 hours.
400
The equation y = 55x represents the rate of the Long Island highway speed limit, in miles per hour. Let x represent the number of hours driven and y represent the total miles driven.
How long was Francis driving if he drove 247. 5 miles at the speed limit.
Francis drove for 4.5 hours.
400
What is the constant of proportionality of this graph?
k = 1/6
400
A jet ski rental charges tourists for $105 for 3 hours. How many hours would it be if you spent $840 to rent the jet ski? Write and solve the unit rate.
$/js
105/3 = 840/?
24 hours
400
Which is the better deal?
12 pounds of grapes for $6.30
or
24 pack of water for $11.28
Grapes: $0.53 per pound
Water: $0.47 per bottle
Water is the better deal
500
Janine sells 16 apples for $8.00. What is the unit price for each apple?
How much would she earn if she sold 64 apples?
The unit price is $0.50 per apple.
Janine would earn $24 for selling 64 apples.
500
If Jackson ate hamburgers at a rate of 3.5 hamburgers per minute and Jacen ate hamburgers at a rate of 4.7 hamburgers per minute, write an equation that could represent how many more hamburgers Jacen can eat more than Jackson.
y = 1.2x
500
How do you find the Constant of Proportionality?
How can you use it to write an equation.
k = y/x
y = kx
500
A coffee shop sells 462 cups of coffee in 11 hours. How many cups of coffee did it sell in 3 hours? Write and solve the unit rate.
c/h
462/11 = ?/3
126 cups in 3 hours
500
What is the constant of proportionality in this table?
k=2.75