Identifying Proportional Relationships
Graphs of Proportional Relationships
Definition
Ratios and Rates
Solving Proportional Word Problems
100
Are these ratios proportional? 
Yes
100
Is the graph a proportional relationship? Why?
NO
Does not go through the origin
100
A relationship between two quantities where the ratio is constant.
Proportional
100
A recipe calls for 3/4 cup of oats to every 3 cups of sugar. Write the ratio of oats to sugar. Find the value of the ratio.
3/4 : 3
Value: 1/4
100
A pizzeria makes 7 pepperoni pizzas for every 3 cheese pizzas. Yesterday they made 42 pepperoni pizzas. How many cheese pizzas were made?
18 cheese pizzas
200
Is the table proportional?
No. There is no constant.
200
what are 2 ways to tell if a graph is proportional
if the line is straight
goes through the origin
200
a comparison of two quantities using division. It shows how many times one number contains another or how two amounts relate to each other.
Ratio
200
A recipe calls for 3/4 cup of oats to every 3 cups of sugar. Write the ratio of sugar to oats. Find the value of the ratio.
3 : 3/4
Value: 4
200
It costs $45.96 for 3 phone cases. How much would it cost to purchase 8 phone cases?
$122.56
300
Is the table proportional?
Yes it is proportional
300
If the (-2, -7) is on a proportional relationship graph, what is the constant?
k=3.5 (or 7/2)
300
represents the independent variable — the one you control or measure as it passes.
X axis
300
Danielle uses 6 lemons to make 3/4 of a gallon of lemonade. How many lemons does Danielle use per gallon?
8 lemons
300
Which is the best buy?
7 pencils for $1.40
6 pencils for $1.26
How much do you save per pencil?
7 pencils for $1.40 is a better deal.
You save $0.01 per pencil.
400
Find x so that 30:14 is proportional to x:1.54
x=3.3
400
Using this graph, What is the constant of proportionality?
k=1/6
400
A pair of numbers written in a specific order, like (x, y), that tells you a point’s exact location on a coordinate plane. The first number is the x-coordinate (left or right), and the second is the y-coordinate (up or down).
Ordered pair
400
Jayden hiked 3/4 of a mile in 2/3 of an hour. How fast was Jayden hiking per hour?
9/8 mph (or 1 1/8 mph)
400
Juliet’s video of her dog got 24 likes in 18 minutes. How many likes could she expect her video to have in an hour and a half?
120 likes
500
Solve
n=3.8
500
Is this graph proportional? If so, what is the cost per hour?
YES. $50 per hour.
500
where the x-axis and y-axis cross on a coordinate plane.
coordinate plane
500
Fill in the missing values in the ratio table.
500
The library at school is organized by fiction and non-fiction books. There are 3 non-fiction books for every 7 fiction books. How many total books are there if the library has 240 non-fiction books?
800 total books