Constant Proportionality from Tables
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
Alice bought comics. Does the below show a proportional relationship. Why or why not?
Number of comics 2 4 6
Price (dollars) 6 12 18
Yes, it is proportional, because all the unit rates are the same.
Morgan bought 6 small packs of batteries, which held a total of 24 batteries. If she had bought 8 packs of batteries, how many total batteries would she have?
32 batteries total
Find the constant of proportionality: y = 7x
k = 7
4 In N Out Burgers contain 4/3 pounds of beef. How many burgers can be made per pound of beef?
3 burgers can be made per pound.
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
Mrs. Dugger went to the bowling alley. The bowling alley charges $5 for shoe rental and $10 per hour of bowling. The equation to represent the total cost is below.
t = 10h + 5
Is it proportional? Why or why not?
No it is not proportional, because it's not in the form y=kx. It has +5.
Michael's juice recipe uses 12 scoops of juice mix for every 4 liters of water. How many scoops of juice mix would he need if he used 12 liters of water?
36 scoops total
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.
y = 20x
Mr. V only eats vegetables. He buys 8 pounds of broccoli for $9.84. How much does the broccoli cost per pound?
$1.23
A ferry transports bikes to an island. Write k (which is the CoP).
Number of trips (x) 5 6 7
Number of bikes (y) 10 12 14
k = 2 bikes per trip
Fred wrote notes during an exam. Does the table below show a proportional relationship? Why or why not?
Notes (pages) (y) 8 9 10
Time (in hours) (x) 18 19 20
It is not proportional. The unit rate is not the same.
Zachary's time machine needs 14 megawatts of electricity to travel back 7 years. How many megwatts of electricity would he need to travel back 21 years?
He would need 42 megawatts to travel back 21 years.
Daisy made bread. The equation B = 4f shows the number of bread loaves baked 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
Sprinters—Usain Bolt is the fastest sprinter in the world. Patrick thinks he can outrun him. Usain bolt can run 36 miles in 2 hours. Patrick 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 Patrick can only run 12 miles per hour.