Constant Proportionality from Tables
Constant of Proportionality from Graphs
Constant of Proportionality from Words
Constant of Proportionality and Equations
Unit Rates/ Scales
100
Drew paints portraits. Find the constant of proportionality if it is a proportional relationship
Time (in hours) = x Number of portraits = y
1 5
2 10
3 15
5 portraits per hour
100
Does the graph below show a proportional relationship? How do you know?
Yes, because it forms a straight line through the origin and has a constant unit rate
100
Morgan bought 24 batteries packed in 6 equal packs. What is the unit rate per pack?
4 batteries per pack
100
Find the constant of proportionality: y = 7x
k = 7
100
4 In N Out Burgers contain 4/3 pounds of beef. Write an equation that shows the relationship between total pounds of beef and the number of burgers.
y=1/3 x
200
The table shows the amount earned by Harry for selling ice cream. Find k.
Cups Sold = x 3 5 7
Earnings ($) = y 12 20 28
CoP = 4
200
What is K with proper units?
k = 1.2 miles per hour
200
Julie brought 5 pounds of cans to a recycling place and was paid $2. Find the constant of proportionality (cost per pound)
$0.40/pound
200
Double points:
Race to the Top—In Mario Kart 8, Wario can finish 5 laps in 1/4 hour.
Write an equation to represent the relationship between the number of laps and hours.
How many laps could Wario finish in 1.3 hours?
1. y = 20x
2. 26 laps
200
Determine the scale factor between the two drawings below:
1.5 or 1 1/2
300
Fred wrote notes during an exam. Find the CoP (with correct units) if it is a proportional relationship.
Notes (pages) 8 9 10 11
Time (in hours) 18 19 20 21
It is not proportional, there is no CoP.
300
Find the constant of proportionality with correct units
5 gallons per min
300
To make juice, Michael combines 4 liters of water and 12 scoops of juice mix. What is the CoP (scoops per liter)?
3 scoops per liter
300
Daisy made bread. The equation B = 4f shows the number of breads basked based on the amount of flour used. Where B is the number of bread loaves made and f is the cups of flour used. Find the constant of proportionality.
k = 4 loaves per cup
300
Mr. V only eats vegetables. He buys 8 pounds of broccoli for $9.84. If Mr. K went to the same store and wants to buy 17 pounds of broccoli, how much would it cost him?
$20.91
400
A ferry transports bikes to an island. Write k (which is the CoP).
Number of bikes (x) 10 12 14
Number of trips (y) 5 6 7
k = 0.5
400
Find k with proper units.
k = 3 gallons per minute
400
Zachary's time machine needs 14 megawatts of electricity to travel back 7 years. What is the unit rate (megawatts per year)?
2 megawatts per year
400
The number of milk bottles sold can be determined by the equation P = 0.35n, where P is the number of bottles of milk and n is the number of boxes opened. Find the constant of proportionality with correct units.
k = 0.35 bottles per box
400
The blueprint for an apartment unit says that every 1 inch corresponds to 3 yards.
What is the actual area of the bedroom?
20.475 yd2
500
Alice bought comics. Find the k (CoP with correct units) if the table shows a proportional relationship.
Number of comics 2 4 6
Price (dollars) 6 12 18
k = 3 dollars per comic
500
Find the constant of proportionality with correct units
60 miles per hour
500
An item that is 4 feet long is 48 inches long. What is the unit rate per foot?
12 in per foot
500
In a laboratory, scientists performed chemical reactions. The amount of product formed by a reaction can be determined by P = 0.25r, where P is the product and r is the amount of reactants used. Find k with correct units.
k = 0.25 product per reactant
500
Sprinters—Usain Bolt is the fastest sprinter in the world. Marcos thinks he can outrun him. Usain bolt can run 36 miles in 2 hours. Xavier can run 6 miles in 0.5 hours. Who is the fastest runner? Explain how you know.
Usain bolt is faster because he runs at a rate of 18 miles per hour, but Xavier can only run 12 miles per hour