Name ______________________________________
Date _________________
L.O. IWBAT
Compare different representations of proportional situations
Compare two
proportional situations
that are represented on
the same set of axes
Model Problem 1:
The graph shows the average speed
of two cars on a highway.
a) Which car travels faster?
Explain how you know?
b) How much faster does this car travel? Show your work.
Compare two
proportional situations
that are represented on
a graph and in a table
Model Problem 2
Ramona and Josh earn money by babysitting. The amounts
earned for one evening are shown in the table and the graph
below. Who charges more? Explain how you know.
Compare two
proportional situations
that are represented on
a graph and in an
equation.
Model problem 3
Sofia and Myla are comparing how fast they both can run. The
graph represents Sofia’s speed and the equation represents
Myla’s speed. Who runs faster? Explain how you know.
Sofia
Myla
y = 7.5 x
Where x represents the time (in seconds)
and y represents the distance (in meters).
Compare two
proportional situations
that are represented in
a table and in an
equation.
Model Problem 4
Melissa and Colleen are having a competition as to who reads
more. For three nights they both keep track of the number of
pages they read and how many minutes they read. The table
shows Melissa’s statistics and the equation shows Colleen’s. Who
reads more? Explain how you know.
Melissa
Time (in min.) 60 120 180
# of pages
50 100 150
Colleen
y=¾x
where x = # of minutes and
y = total amount of pages
SUMMARY
There are several different strategies you could have used to solve the previous 4 model
problems. However, since our focus has been the constant of proportionality, explain how
the constant of proportionality can help us to solve these problems.
Practice HW: Compare proportional situations
1)
The table and graph show the amount of rainfall for 2 different days. Which day had
a greater rate of rainfall? Explain how you know.
2) The graph shows the cost of purchasing Tee Shirts from Store A. The equation
represents the total cost (y) for buying (x) tee shirts from Store B. Which store has the
better buy? Explain how you know.
Store A
Store B
y = 8.5x
3) The Guzman and Hashimoto families each took a 4-hour road trip. The distances traveled
by each family are shown in the table and the graph below. Which family averaged the
faster rate?
4) The table and the graph show the hourly rate to rent a bicycle at two different stores.
Which store has the better rate?
Great
Time
(hours)
1.5
2
2.5
3
Bikes
Cost
($)
11.25
15
18.75
22.50
Pushy Pedals
5) Each week Randy and Charleine put money into their savings. At the end of 6 weeks,
Randy has saved $94.50. The equation represents what Charleine has saved (y) in
(x) weeks: y = 16.25x
Who has a better rate of saving? Explain how you know.
6) Ms. Posluszny wants to know which pizza place makes the cheesiest pizzas. The
representations below represent the number of ounces of cheese used per pizza. Write
the names of the pizza places in order beginning with the one that has the cheesiest
pizza.
Nick’s Pizza
Tyff’s Pizza
y = 6x
Kevin’s Pizza
# of
2
Pizzas
Cheese 14
(oz.)
Alexa’s Pizza
4
6
28
42
y
= 7.5
x
7) A person clocked the speed of two race cars. The rates are represented in the equations
below. x represents the time in hours and y represents the distance in miles. Which car
was faster?
Car A: y = 120x
Car B:
y
= 130
x