Name: ____________________________
Ratios and Proportions – Slope as Constant Rate of Change
1
The graph shows the average speed of two cars on the
highway.
Date: _________
PreAlgebra
Sheet # 02 - 11
Part G Is there a way to determine which car is moving faster in
the graph below? Justify your response.
2
The graph shows two cars that have left at the same
time to a certain destination. Car F started the trip 60
miles ahead of Car E.
Part A Do the two graphs represent proportional relationships?
Part B What does (2, 120) represent?
Part C Find the constant unit rate for Car A in miles per hour.
Part A Do the two graphs represent proportional relationships?
Answer ____________ miles per hour
Part D What does (1.5, 67.5) represent?
Part E Find the constant unit rate for Car B in miles per hour.
Part B Make a conjecture about which car is moving at a faster
rate of speed.
Part C Determine the constant rate of change for each car in
order to test your conjecture from Part B.
CAR F
Car E
Answer ____________ miles per hour
Part F Which car is moving at a faster rate of speed?
Answer ____________ mph
Answer ____________ mph
3
Part A Is the relationship shown in the
graph proportional? If so, determine the
constant unit rate.
5
Part B Determine the slope of the line.
Part C Discuss what the slope means as
the constant rate of change.
Part C Discuss what the slope means as
the constant rate of change.
Part A Is the relationship shown in the
graph proportional? If so, determine the
constant unit rate.
6
Part A Is the relationship shown in the
graph proportional? If so, determine the
constant unit rate.
Part B Determine the slope of the line.
Part B Determine the slope of the line.
Part C Discuss what the slope means as
the constant rate of change.
How can you find the unit rate of
a graph that goes through the
origin?
8
Explain the connection between
the unit rate and the constant rate
of change in proportional
relationships.
9
How is the constant rate of
change related to slope?
Part A Is the relationship shown in the
graph proportional? If so, determine the
constant unit rate.
Part B Determine the slope of the line.
4
7
Part C Discuss what the slope means as
the constant rate of change.
10
All linear relationships have a
constant rate of change, but do
all linear relationships have a
constant unit rate? Explain.
Name: ____________________________
Date: _________
Sheet # 02 - 12
Ratios and Proportions – Slope as Constant Rate of Change
PreAlgebra
The cost of renting video games from Game
The number of meters Jessie can bike over
1 Central is shown in the table.
2 time is shown in the table.
Part A Plot the ordered pairs on the coordinate plane.
Part A Plot the ordered pairs on the coordinate plane.
Part B Is the relationship between the number of games Part B Is the relationship between the number of meters
and the cost proportional?
traveled and the seconds proportional?
Part C What does the ordered pair (1, 3) represent? Is
this the constant unit rate? Explain why or why not.
Part C What does the ordered pair (1, 6) represent? Is
this the constant unit rate? Explain why or why not.
Part D What is the slope of the line you drew?
Part D What is the slope of the line you drew?
Answer: _____________
Part E Discuss what the slope means as the constant
rate of change.
Answer: _____________
Part E Discuss what the slope means as the constant
rate of change.
How can you find the unit rate on a graph that goes through the origin?
What is the relationship between slope and constant rate of change?
Is there a way to find the constant rate of change from the table without having to create the graph?
3
A computer programmer charges
customers per line of code
written. Fill in the blanks with
the amount of change between
consecutive numbers.
6
The table shows the number of
students that buses can transport.
9
The constant rate of change for
the relationship shown in the
table is $8 per hour. Find the
missing values.
PART A Fill in the blanks with the amount
of change between consecutive numbers.
Part A Is the relationship shown in the
table proportional?
PART B Label the diagram below with the
terms change in lines, change in dollars,
and constant rate of change.
Part B Use the table to find the constant
rate of change in students per school bus.
x = ________ y = ________ z = ________
10
The information in the table
represents a constant rate of
change. Find the missing value.
Part C Is there a constant unit rate? If so,
what is it?
The ______________________ is $20 per
line of programming code.
7
4
The table below shows the
amount of money the Class of
2018 makes washing cars for a
fundraiser. Use the information
to find the constant rate of
change in dollars per car.
Find the constant rate of change
for the table in dollars per
minute.
A
30
C
105
B
90
D
120
11
Which value would complete the
table to make the relationship
between the two quantities
proportional?
Part A Is the relationship shown in the
table proportional?
Part B Use the table to find the constant
rate of change in cost per minute.
The table shows the number of
miles a plane traveled while in
flight. Use the information to
find the approximate constant
rate of change in miles per
minute.
44.8
C
89.6
B
67.2
D
56
12
Answer _________ dollars per car
5
A
Use the information in the table
to find the constant rate of
change in seeds per apple.
Part C Is there a constant unit rate? If so,
what is it?
8
Make a table where the constant
rate of change is 6 inches for
every foot.
Answer _________ miles per minute
A
10
1
C
40
4
B
1
10
D
4
40