Constant of Proportionality In Words
Constant of Proportionality Equations
Tables and Graphs
Proportional or Not?
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. What is the unit rate of this proportional relationship?
900 basketballs per hour
100
Which line represents a proportional relationship? Explain.
All 5 lines represent a proportional relationship because they are straight (linear) and pass through the origin.
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. She earns $1,050 for working 7 weeks. Is this a proportional relationship?
Yes this is proportional. Beverly makes $150 per week.
200
Which relationship has the constant of proportionality? Explain.
y = 7x
or
?
The graph has a greater COP of 25. The equation has a COP of 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 and a one-time fee of $24. Is this a proportional relationship?
For one day rental, they charge $104.
For two days rental, they charge $184.
No this is not a proportional relationship because of the one time fee.
300
Which has the greater constant of proportionality? Explain.
y = 4.2x
4 pounds of walnuts costs $18.
The price of walnuts is the greater COP because 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 or
$325 for 5 hours. Is this a proportional relationship? How do you know?
No, this is not proportional because there is not a constant of proportionality.
400
Which has the smaller constant of proportionality? Explain.
The graph?
or the word problem: Jesse completed 10 laps in 18 minutes. How many laps did he run in 1 minute?
The word problem has a smaller COP.
The graph is 2/3 of a lap per minute, or 6/9 of a lap per minute.
The Word problem is 5/9 of a lap per minute.
5/9 < 6/9
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
Find the constant of proportionality of line e. Then write an equation for the relationship.
k = 1/3
y = 1/3x
500
How many lines on this graph are representing proportional relationships?
Find the constant of proportionality of each line.
All 4 lines represent a proportional relationship.
line m = 2
line n = 1/2
line j = -1
line k = -3
500
Which relationship has the greater constant of proportionality? The table or the graph. How do you know?
Well A Pumps water at a faster rate at 2.75 barrels per hour. Where Barrel B pumps water at 2.5 barrels per hour.