Calculating Unit Rates
Identifying Proportional Relationships
Constant of Proportionality
Interpreting Graphs & Solving Problems
Multiple Representations
100
If a car travels 300 miles in 5 hours, what is its speed in miles per hour?
60 miles per hour
100
A relationship is proportional if its graph is a straight line that passes through this specific point.
The origin (0,0)
100
Write the equation for a proportional relationship, where k is the constant of proportionality.
y = kx
100
On a graph representing the cost of apples, what does the point (0, 0) mean in the context of the problem?
Zero apples cost zero dollars
100
During the fall a pumpkin patch advertises four pumpkins for $11.00. Which equation below represents this proportional relationship?
A. y = 4/11x
B. y = 2.75x
C. y = 0.36x
D. 11y = 4x
B. y = 2.75x
200
A store sells 12 ounces of trail mix for $4.80. What is the unit rate (cost per ounce)?
$0.40 per ounce
200
Proportional or Not Proportional?
Not Proportional
200
In the equation y=7.5x, what is the constant of proportionality?
7.5
200
What does the coordinate point (6,48) represent?
Six pizzas will contain 48 slices of pizza.
200
Which of the following equations best represents the relationship?
A. y=7.6x
B. y=684x
C. y=0.13x
D. y=76x
D. y=76x
300
An artist uses 3/4 cup of paint to cover 5/8 of a canvas. What is the unit rate in cups of paint per whole canvas?
1⅕ or 1.2 cups of paint per canvas
300
Proportional or Not Proportional?
Not Proportional
300
Find the constant of proportionality.
k=7
300
How long did it take Seth to get to the store?
18 minutes
300
Use the conversion factor of 1 kilogram = 2.20462 pounds.
If a recipe calls for 2 kilograms but your kitchen scale uses pounds, how many pounds of sugar will you need?
4.409 pounds of sugar
400
Chick-Fil-A was selling 3 boxes of chicken fingers for $25.90.
Jack's was selling 2 boxes of chicken fingers for $11.07.
Which restaurant has a higher unit price?
Chick-Fil-A
400
True or False? The number of hours is proportional to the number of money earned.
True.
400
Sam works after school at a hardware store. He earns $15 per hour.
a) Find the constant of proportionality in this situation.
b) Write an equation to represent the relationship.
a) k=15
b) y=15x
400
Kiara was walking to her friend’s house. What does the horizontal line from 2 to 4 seconds represent?
She was stopped for 2 seconds. Her distance remained the same.
400
The equation C = 2.5g relates the cost (C) of gas to the number of gallons (g). What is the ordered pair on the graph that represents the cost of one gallon of gas?
(1, 2.5)
500
A recipe calls for 2 cups of flour for every 3 eggs. If you use 7 eggs, how many cups of flour do you need?
4 ⅔ or 4.67 cups of flour
500
Create a table and determine if the scenario is proportional or not.
A plumber charges $50 to come to your house and $25 an hour to work.
Not proportional.
500
It costs $12.00 for a 24 pack of soda.
a) Find the constant of proportionality for this situation.
b) Write an equation to represent the relationship.
a) k=0.5
b) y=0.5x
500
The graph of a proportional relationship passes through (5,30). Write the equation that represents this relationship.
y=6x
500
A proportional relationship is described by the equation y = 15x, where x is the number of hours and y is the total profit in dollars. How many hours would it take to make a profit of $225?
15 hours