Unit Rate
You buy 3 notebooks for $6. What is the unit rate per notebook?
$2 per notebook
A table shows that when x=2; y=6
If the relationship is proportional, what is the constant of proportionality?
k=3 (because y=3x)
Ava volunteers at a pet store. She notices that 9 pounds of cat food can feed 6 cats for one week.
a. Write an equation to represent the relationship between the amount of food (y) and number of cats (x).
b. How many pounds of food would she need to feed 10 cats for a week?
a. y=1.5x
b. 15 pounds of cat food.
A 12-pack of soda costs $5.40, and a 24-pack costs $9.60. Which is the better buy?
24-pack ($0.40/can vs. $0.45/can)
The graph showing Emma’s smoothie sales passes through the points (2, 10) and (5, 25).
a. Is this relationship proportional?
b. Find the constant of proportionality.
c. Write the equation that represents the relationship.
a. Yes - Straight line and through the origin
b. 10/2 = 5 k=5
c. y=5x
A car travels 240 miles on 8 gallons of gas. What is the unit rate in miles per gallon?
30 miles per gallon
If the equation is y=2.5x, what is the constant of proportionality?
k=2.5
Noah is cooking pancakes for breakfast. His recipe uses 2 cups of mix for every 1.5 cups of milk.
a. Write the ratio of mix to milk.
b. If Noah wants to make 6 cups of mix, how much milk will he need to keep the recipe proportional?
a. 2 cups of mix : 1.5 cups of milk
b. 4.5 cups of milk
Cereal A costs $3.50 for 10 ounces.
Cereal B costs $4.80 for 12 ounces.
Which is the better buy?
Cereal A ($0.35/oz vs. $0.40/oz
The graph of Sofia’s distance over time passes through (1, 4.5), (2, 9), and (3, 13.5).
a. Find the constant of proportionality.
b. Write an equation that represents her distance (y) in kilometers after x hours.
a. 4.5/1 = 4.5 k=4.5
b. y = 4.5x
You buy 12 apples for $9.60. What is the cost per apple?
$0.80 per apple
A faucet fills 9 gallons of water in 12 minutes.
Assuming the relationship is proportional, what is the constant of proportionality in gallons per minute?
k=9/12 =0.75 gallons per minute
Lily’s family drives from her hometown to the beach. They travel 180 miles in 3 hours at a constant speed.
a. What is the constant of proportionality (miles per hour)?
b. Write an equation to show the relationship between distance (y) and time (x).
c. How far will they travel in 5.5 hours?
a. k=180/3 = 60 mph
b. y=60x
c. y=60(5.5)=330 miles
Bag of chips A: 14 oz for $4.48
Bag of chips B: 10 oz for $2.90
Which is the better buy?
Bag B ($0.29/oz vs. $0.32/oz)
How do you know if a graph is proportional?
It will be a straight line and go through the origin.
A 6-pack of juice boxes costs $3.54. What is the price per juice box, rounded to the nearest cent?
$0.59 per juice box
The graph of a proportional relationship passes through the points (3, 7.5) and (8, 20).
What is the constant of proportionality?
k= y/x =7.5/3 = 2.5
Olivia is preparing for a charity 10K. She tracks her pace and finds she can run 3 kilometers in 18 minutes.
a. What is her constant of proportionality (minutes per kilometer)?
b. Write an equation to represent the relationship between time (y) and distance (x).
c. How long will it take her to run 7 kilometers at the same pace?
a.k= 18/3 = 6 minutes per km
b. y=6x
c. y=6(7)=42 minutes
Store A sells 5 pounds of strawberries for $15.
Store B sells 3 pounds for $8.
Which is the better buy?
Store B ($2.67/lb vs. $3/lb)
What is the equation for finding the constant of proportionality?
y/x
You earn $78 for working 6.5 hours. What is your hourly rate?
$12 per hour
A car travels 156.25 miles in 3.5 hours at a constant speed.
Find the constant of proportionality and interpret it.
k=156.25/3.5 =44.64 miles per hour (rounded)
Interpretation: The car travels about 44.64 miles for every 1 hour.
Carter is making fruit punch for a party. His recipe calls for 6 cups of juice for every 2 cups of soda.
If he wants to make a total of 32 cups of punch, how many cups of juice and soda should he use?
24 cups of juice, 8 cups of soda
A grocery store sells three sizes of granola:
Small bag: 18 ounces for $5.94
Medium bag: 32 ounces for $9.12
Large bag: 48 ounces for $14.88
Which bag is the best buy, and what is the unit price per ounce for each option?
Small bag → $5.94 ÷ 18 = $0.33/oz
Medium bag → $9.12 ÷ 32 = $0.285/oz
Large bag → $14.88 ÷ 48 = $0.31/oz
Best buy: Medium bag at $0.285 per ounce
What is the equation to determine if a situation is proportional?
y = kx