Proportional Relationships - Ms. Schmidt's Math Class
Transcript of Proportional Relationships - Ms. Schmidt's Math Class
Proportional Relationships
The graph should be linear. For a directly proportional relationship, the
graph will always be a straight line through the origin.
NAME:______________________
CLASS:_____________________
TEACHER: Ms. Schmidt _
Computing Unit Rate Classwork Day 1
Vocabulary
Ratio - ______________________________________________________________________________
Unit Rate – __________________________________________________________________________
____________________________________________________________________________________
Example 1: How fast is our class?
Trial Number of Papers
Passed
Time
(in seconds)
Ratio of Number of
Papers Passed to Time
Rate Unit
Rate
1
2
3
Find the unit rate of each:
1) 216 meters in 8 seconds– how many meters for 1 second?
2) Express the ratio of $10 for 8 fish as a unit rate (1 fish).
3) $2,702 for 28 people- how much money for 1 person?
Express each ratio as a fraction in simplest form:
4) 27 rooms to 48 windows 5) 3 gallons to 15 quarts
A unit rate is a rate per one given unit; such as 34 miles per 1 gallon
Computing Unit Rate Classwork Day 1
Which is the better price?
6) Six candy bars for $2.62 or eight bars for $3.40?
7) Paint brushes that sell in a packet of one dozen for $6.46 or eighteen for $9.90?
8) If you spend $11.13 for 8 gallons of gasoline, how much would you spend on 14 gallons?
TRY THESE:
1) Mr. K needs help solving this problem. A hot dog truck sells 9 hot dogs for $11.25.
a) Find the unit rate
b) If he wants to buy 3 hot dogs for Mrs. Trantino, how much will it cost?
2) Write in simplest form: 13 diamonds to 52 cards
3) Which is the better price?
32 ounces for $3.84 or 40 ounces for $4.40
More Practice:
Find the unit rate of each:
1) The Seneca’s Student Government sold $75 worth of tickets for a talent show in 3 hours. How many tickets
did they sell in one hour?
hourshours
$$
2) At Six Flags, 1,473 people entered the park in 3 hours. How many people entered the park in 1 hour?
hours
people
hours
people
3) A wedding a Villa Lombardi’s cost $9,750 for 150 people. How much does Villa Lombardi’s charge per
guest?
4) April showers bring May flowers! If 3 inches of rain fell in 5 hours, how many inches fell per hour?
5) You can buy 4 apples at Stop and Shop for $0.96. You can buy 6 of the same apples at Pathmark for $1.50.
Which store has the better buy?
Computing Unit Rate Classwork Day 1
6) If a runner ran 102 meters in 12 seconds, how many meters did he/she run per second?
7) Ticketmaster sold 1200 tickets to the Mets-Yankees game in 3 hours. How many tickets were sold is one
hour?
Which is the better bargain? Find the unit price for each and compare them.
8) Pens: $4.50 for 3 pens or $3.20 for 20 pens 9) Pencils: 16 for $8.32 or 35 for $17.15
10) Lucy went away on vacation for 10 days and when she came home she had 280 emails. How many emails
did she get per day?
11) Derek just got a new I-Phone and downloaded 348 songs in 6 hours. How many songs did he download per
hour?
12) Ryan and his brother are comparing the prices of two brands of cereal. Frosted Flakes costs $2.25 for a 15-
ounce box. Lucky charms costs $3.90 for a 30-ounce box. Which brand is more expensive and by how much
per-ounce?
13) Gas mileage is the average number of miles you can drive a car per gallon of gasoline. A test of a new car
resulted in 2,250 miles being driven using 125 gallons of gas. Find the new car’s gas mileage.
14) The table shows the prices that Mrs. Dragotta paid at 3 different gas stations. Complete the table to
determine which gas station had the better price per gallon.
Gas Station Gallons Price Price per Gallon (Show work here)
Hess 15 $43.50
Coastal 10 $29.40
Amoco 12 $35.88
Proportional Relationships Classwork Day 2 Vocabulary
Constant of Proportionality - The value of the ratio of quantities in a proportional relationship. This value is
also equivalent to the unit rate.
Understand what the phrase proportional to means. A very common misconception is that two variables are
directly proportional to if one increases as the other increases. Two variables are said to be directly proportional
if, and only if, their ratio is a constant for all values of each variable. Therefore when one variable is divided by
the other, the answer is always a constant. They have the same unit rate.
Directly NOT Directly
Proportional Proportional
Independent Variable (Domain x)___________________________________________________________
Dependent Variable (Range y)______________________________________________________________
Look at the tables and determine if the quantities given are in a proportional relationship.
****In order to test for proportional relationships, quantities must have equivalent ratios.
**** Compare each ratio to see if they are equivalent. Is there a constant rule? If yes, it is proportional.
****Are the cross products equal?
Example 1) Example 2)
Proportional? Yes or No Proportional? Yes or No
Using a ratio to identify a unit rate-Practice 1) Gas Mileage 2) Cooking Times
Miles 200 300 400
Gallons of gas used 10 15 20
Proportional yes/no Proportional yes/no
Unit Rate(miles per gallon) = Unit Rate(pounds per hour) =
3) Paint Coverage 4) Grapes per pound
Proportional yes/no Proportional yes/no
Hour $
3 90
4 120
6 180
Hour Miles
1 30
2 60
3 120
Weight of Turkey(lb) 16 14 10
Cooking Time (hour) 4 3.5 2.5
Amount of Paint (gallons) Area Covered (square feet)
1/2 2,000
3/4 3,000
3 12,000
4 18,000
Grapes (pound lb) Cost (per lb)
5 $6.00
3 $3.60
1/4 $1.20
Proportional Relationships Classwork Day 2
Find the Unit Rate and Missing Value.
1) Babysitting Pay-Salary per hour 2) Dog Biscuits
Unit Rate in words ______________________ Unit Rate in words ______________________
Unit Rate($ per hour) _______ Unit Rate (Cost per biscuit)______
3) Texting Prices 4) Calories burned for 130 lb. woman running 5 mph
Unit Rate in words ______________________ Unit Rate in words ______________________
Unit Rate (cost per text) _______ Unit Rate (calories per hour)______
Extra Problems:
Determine whether each table forms a proportional relationship. (SHOW ALL WORK)
*Remember the table must have equivalent ratio.
1) 2) 3)
Proportional? yes or no Proportional? yes or no Proportional? Yes or No
4)
5)
6)
Hours (h) 2 10 16
Pay (p) $11 $55
Biscuits (lb) 3 10 12
Price $1.65 $5.50 $9.90
# of texts 200 300 50
Pay (p) $150 $225 $18.75 Length of workout (hours) .5 .75 .25
Calories burned 236 354 1,416
x 1 2 4 7 9
y 5 9 17 29 37
x 2 4 6 8 10
y 1.5 3 4.5 6 7.5
x y
1 3
2 6
3 9
4 12
x y
2 3
3 5
4 7
5 9
x 1 2 3 4 5
y 2 8 16 32 64
x 1 3 5 7 9
y
Proportional? yes or no Proportional? yes or no Proportional? yes or no
Identifying Proportional Relationships Classwork Day 3
Vocabulary
Unit Rate______________________________________________________________________________
Constant of Proportionality y = cx or y = kx___________________________________________________
Constant rate of change (slope) ____________________________________________________________
Origin_________________________________________________________________________________
*Proportional relationships can be represented on a coordinate plane. A graph of every proportional
relationship will be a straight line that includes the origin, the point (0,0). Can you draw this?
1) The graph shows the relationship between the time it takes a turtle to walk and its distance.
How far does it travel at 0 hours?_________miles
How far does it travel at 1 hour?__________miles
How far does it travel at 2 hours?_________miles
How far does it travel at 3 hours? ________miles
How far will it travel in 6 hours?_________miles
What does the point (2, 2) mean?_________________
What is the unit rate (1,r)? ______
Since this graph goes through the origin and the
unit rate is constant it is a proportional relationship.
Determine whether each graph is proportional.
2) 3)
Yes or No- Justify______________________________ Yes or No- Justify_________________________
Sod Sales
Area (sq. ft)
Tota
l C
ost
($)
Turtle Speed
Time (hr)
Distance
(miles)
Mowing Lawns
Lawns
Profit
($)
0
60
120
180
240
300
360
0 1 2 3 4 5 6 7 8
0
50
100
150
200
250
300
350
400
0 1 2 3 4 5 6 7 8
Identifying Proportional Relationships Classwork Day 3
4)
7) The graph shows distances traveled for a bike-a-thon.
Use the information displayed in the graph to find out
how many miles the participant rides in 11 hour.
5) (0,0), (1,2), (2,4), (3,6) Proportional? Yes or No
(Direct Variation)
Justify_____________
__________________
__________________
6) (0,4), (1,6), (2,8), (3,10) Proportional? Yes or No
(Direct Variation)
Justify_____________
Justify______________
__________________
__________________
Tricycle-a-thon
Miles
8) A student trying to save the Holtsville
Ecology site was getting signatures on a
petition at a rate of 30 signatures a day. At
this rate, how many signatures will he have
in 1 week? Petition
Days
Signatures
What is the unit rate? (miles per hour)
______________
Hour
Road Trip
Hours
a) Is the graph showing a proportional
relationship?
b) Speculate what might have happened
during the 3rd and 4th hour of the trip.
c) What is the average speed from hour 1
to hour 3?
d) What is the average speed for the
entire trip?
Mil
es
Hour
Identifying Proportional Relationships Classwork Day 3
9) The graph shows your wages for mowing
lawns during the summer. How many lawns will
you mow if you earned $390?
10) 11)
Why? Why?
Proportional? yes or no Proportional? yes or no
12) Isaiah sold candy bars to help raise money for his scouting troop. The table shows the amount of candy he
sold to the money he received.
Is the amount of candy bars sold proportional to the money Isaiah received? How do you know?
Example 1: From a Table to Graph
300
270
240
210
180
150
120
90
60
30
Lawns
Wage
($)
Mowing Lawns
Proportional? Yes or No Proportional? Yes or No Unit Rate________
Identifying Proportional Relationships Homework Day 3
1) Complete the table below. 2) Using the graph, answer the following questions.
Yogurt Costs
a) What is the unit rate?
b) How many inches will be 18 yards?
Show Work for #1 here
3) During Jose’s physical education class today, students visited activity stations. Next to each station was a
chart depicting how many calories (on average) would be burned by completing the activity.
Calories burned while Jumping Rope
a) Is the number of Calories burned proportional to time? How do you know?
b) If Jose jumped rope for 6.5 minutes, how many calories would he expect to burn?
Amount of
Yogurt (c)
Price
($)
50 37.5
100
96 72
150
4) Multiply:
7 ∙ 7
3
5) What is 4 12
5 as
an improper
fraction?
6) Order from least
to greatest 2
1, 7%,
0.68
7) Evaluate: x∙y
for x = 3
1 and y = 27
8) What is a solution
of 04
3 x ?
0
36
72
108
144
180
020406080
100120140160180200
0 1 2 3 4 5 6
Nu
mb
er
of
Inch
es
Number of Yards
YARDS AND INCHES
Unit Rate as the Constant of Proportionality in an Equation Classwork Day 4
Find the Constant and Write the Formula y = cx or y = kx
When the ratios of two quantities are always the same, the quantities are proportional. The value of the
ratio is called the constant of proportionality(k or c). This value is also equivalent to the unit rate.
.5 .5
Vocabulary
Constant-_______________________________________________________________________________
Coefficient - _____________________________________________________________________________
Variable-________________________________________________________________________________
Identify the constant (Hint-circle the word after the word “per” because that is your x(input).)
Find the constant of proportionality for each table/graph and write the equation of the direct variation.
1) yards of cloth per blanket
Constant of proportionality
(c) = _____
Equation_________________
Yards (y) 16 32 40
Blankets (b) 8 16 20
2) pay per hour
Constant of proportionality
(c) = _____
Equation______________
Hours (h) 2 10 16
Pay (p) $11 $55 $88
3)
Constant of proportionality
(c) = _____
Equation_________________
4)
0.5 is the constant of
proportionality. The height
is half the width. h = .5w Constant of Proportionality is the same as unit rate (slope).
x
yk
______ is the constant of
proportionality.
h = ____w
The graph to the right shows the distance (in ft.) ran by a Jaguar.
a) What does the point (5, 280) represent in the context of the
situation?
b) What does the point (3, 168) represent in the context of the
situation?
c) Is the distance run by the Jaguar proportional to the time?
Explain why or why not.
d) Write an equation to represent the distance ran by the Jaguar.
Explain or model your reasoning.
Dis
tance
(ft
)
Jaguar’s Run
Unit Rate as the Constant of Proportionality in an Equation Classwork Day 4
When two values are directly proportional, the value of the output (y) divided by the input (x) will always have
the same value. This value will be the coefficient of the input, x.
Find the constant of proportionality (unit rate) in each of the relationships that follow:
1) y = 3x 2) y = x3
1 3) y = x 4) y =
2
3x
c = ________ c = _________ c = _________ c = __________
If you are given a table or a graph, you can find the constant of proportionality (slope) by dividing the output, y,
by the input, x. (x
y)
Find the constant of proportionality in the chart and graph below. Next, write the equation for the situation.
1) Find the constant of proportionality. x
y
Write the equation that satisfies this table.
x y
0 0
1 4
2 8
3 12
2) Find the constant of proportionality. x
y
Write the equation that satisfies this graph.
3) Find the constant of proportionality. x
y
Write the equation that satisfies this table. Before you
begin, which value do you think is the output?
Hours (h) 2 10 24 40
Pay (p) $16 $80 $192 $320
4) Find the constant of proportionality.
Write the equation that satisfies this graph.
y
x
y
x
= c,
Then write your equation as
y = ___ x
Constant/slope
__________
Equation
____________
Constant/slope
__________
Equation
____________
Unit Rate as the Constant of Proportionality in an Equation Classwork Day 4
5) Find the constant of proportionality. x
y
Write the equation that satisfies this table.
x y
0 0
1 3
2 6
3 9
6) Find the constant of proportionality. x
y
Write the equation that satisfies this graph.
7) Find the constant of proportionality.
Write the equation that satisfies this table. Before you
begin, which value do you think is the output?
Hours (h) 2 10 24 40
# of rooms
painted (p)
1.5 7.5 18 30
8) Find the constant of proportionality.
Write the equation that satisfies this graph.
9) If the constant of proportionality is 3.5, what is
the equation?
10) A truck driver has travelled 350 miles in 5
hours. Write an equation that represents his
distance travelled per hour.
11) The cost of a certain vegetable is 0.59 per
pound. Write an equation to represent this
situation, using c to represent the cost and p,
for pounds.
12) The new data plan offers 2MB of data for $30.
Write an equation to represent this situation,
using c to represent the cost and d, for data.
y
x
y
x
x
y= k,
Then write your equation as
y = ___ x
Constant/slope
__________
Equation
____________
Constant/slope
__________
Equation
____________
Unit Rate as the Constant of Proportionality in an Equation Homework Day 4
K or c = constant of proportionality x
y
Find the Constant (unit rate/slope) and Write the Formula y = kx or y = cx
1) wages per day
Constant of proportionality
(k) = _____
Equation___________________
Days
(d) 5 10 15
Wages
(w) $51.25 $102.50 $153.75
2) price per pound
Constant of proportionality
(k) = _____
Equation___________________
Pounds 4 5 6
Price $7.96 $9.95 $11.94
3) pounds per bag
Constant of proportionality
(k) = _____
Equation___________________
Bags (b) 3 8 11
Dog
Food (lb)
(d)
7.5 20 27.5
4) 5)
Constant of proportionality (k) = _____ Constant of proportionality (k) = _____
Equation___________________ Equation___________________
6) A bakery can produce 120 cookies for every 3 hours. What is the constant of proportionality? What is the
equation that represents this situation?
Oranges (f)
Fruit Price per Pound
Pri
ce (p
)
Tickets (t)
Dance Tickets
Pro
fit
(p)
7) The following table shows the amount of candy and price paid.
a) Is the cost of candy proportional to the amount of candy?
b) Write an equation to illustrate the relationship between the amount of candy and the cost. _______________
c) Using the equation, predict how much it will cost for 12 pounds of candy?
d) What is the maximum amount of candy you can buy with $60?
8) Plot the following points on a coordinate grid.
(2,2), (4,4), (6,6), (8,8)
Find the constant of proportionality ____
What is the equation?_____________
9) Plot the following points on a coordinate grid. (3,1), (6,2), (9,3)
Find the constant of proportionality ____
What is the equation?_____________
10) Create a real-life question that has a constant of
proportionality that is a whole number. Be sure to
write the equation and explain what it means.
11) Create a real-life question that has a constant of
proportionality that is a fraction. Be sure to write the
equation and explain what it means.
Write the Constant of Proportionality as a Table Classwork Day 5
Write the Equation (y=cx) from a table
Complete the following tables. Using the table of values, write the equation on the line.
1) 2) 3)
X Y
3 6
4 8
5 10
6 12
7 14
8 16
9
10
4) 5) 6)
7) How is #5 different from all the other tables? Can you figure out the rule?
X Y
2 6
3 9
4 12
5 15
6 18
7 21
8
9
X Y
1 10
2 20
3 30
4 40
5 50
6 60
7
8
X Y
2 10
3 15
4 20
5 25
6 30
7 35
8
9
X Y
1 5
2 8
3 11
4 14
5 17
6
7
8
X Y
6 3
8 4
10 5
12 6
14 7
20
30
x
yc
Write the Constant of Proportionality as a Table Classwork Day 5
8) Given the equation of a line, y = 4x, 9) Given the equation of a line, y = 2x + 1,
complete the following table. complete the following table.
10) Fill in the blanks to the right.
11) Write an equation to find the price for 12) Write an equation to find the amount for any
any amount of minutes. amount of days
x y
1
2
3
4
x y
2
8
10
11
Minutes (m) Price (p) in $
100 $10
500 $50
1,000 $100
1,500 $150
Art Sales
Days
Dollars
(hundreds)
Walking
Time (hr)
Distance
(miles)
Constant/slope (c) __________
Equation ________________
Constant/slope (c) __________
Equation ________________
Constant/slope (c) __________
Equation ________________
Not a direct
Variation (not a
constant of
proportionality)
x
yc
Write the Constant of Proportionality as a Table Homework Day 5
y= cx
c = constant of proportionality
Write the linear equation that gives the rule for this table. Write your answer as an equation with y first,
followed by an equals sign.
1) 2) 3) 4)
Constant__________ Constant__________ Constant__________ Constant__________
Equation___________ Equation____________ Equation_________ Equation_________
5) Write the equation for the relationship shown in the graph. Use whole numbers:
0
2
4
6
8
10
0 1 2 3 4 5 6 7 8 9 10
Review- Show work on separate paper. Don’t be afraid of all the words.
6) Randy is planning to drive from New Jersey to Florida. Randy recorded the distance traveled and the total
number of gallons used every time he stopped for gas.
Assume miles driven are proportional to Gallons Consumed in order to complete the table.
x y
1 16
2 32
3 48
4 64
x y
1 19
2 38
3 57
4 76
x y
3 9
7 21
11 33
15 45
x y
1 11
2 22
3 33
4 44
Write the Constant of Proportionality as a Table Homework Day 5
7) Andrea is a street artist in New Orleans. She draws caricatures (cartoon-like portraits of tourists). People
have their portrait drawn and then come back later to pick it up from her. The graph below shows the
relationship between the number of portraits she draws and the amount of time in hours needed to draw the
portraits.
a) Write several ordered pairs from the graph and explain what each
coordinate pair means in the context of this graph.
b) Write an equation that would relate the number of portraits drawn to the
time spent drawing the portraits.
c) Determine the constant of proportionality and explain what it means in this situation.
8) The graph below shows the amount of time a person can shower with a certain amount of water.
a) Can you determine by looking at the graph whether
the length of the shower is proportional to the number of
gallons of water? Explain how you know.
b) How long can a person shower with 15 gallons of
water and with 60 gallons of water?
c) What are the coordinates of point A? Describe point A
in the context of the problem.
d) Can you use the graph to identify the unit rate?
e) Plot the unit rate on the graph. Is the point on the line of this relationship?
f) Write the equation to represent the relationship between the number of gallons used and the length of a
shower.
Shower Water Usage
Using Unit Rate as a Scale Factor Classwork Day 6
Explain what a point (x,y) on the graph of a proportional relationship means in terms of the
situation, with special attention to the points (0,0) and (1,r) where r is the unit rate.
Do Now - Write an equation that will model the proportional relationship given in each real world situation.
1) There are 3 cans that store 9 tennis balls. Consider the number of balls per can. a. Find the constant of proportionality for this situation. __________ Write in words__________________
b. Write an equation to represent the relationship. ____________
2) In 25 minutes Li can run 10 laps around the track. Consider the number of laps she can run per
minute. a. Find the constant of proportionality in this situation.
b. Write an equation to represent the relationship. ______________
Examples
1) On average, Susan downloads 60 songs per month. An online music vendor sells package prices for songs
that can be downloaded on to personal digital devices. The graph below shows the package prices for the most
popular promotions. Susan wants to know if she should buy her music from this company or pay a flat fee of
$58.00 for the month offered by another company. Which is the better buy?
2) Ms. Robinson decided to make juice to serve along with the pizza at the Student Government party. The
directions said to mix 2 scoops of powdered drink mix with a half a gallon of water to make each pitcher of
juice. One of Ms. Robinson’s students said she will mix 8 scoops with 2 gallons of water to get 4 pitchers. How
can you use the concept of proportion to decide whether the student is correct?
Using Unit Rate as a Scale Factor Classwork Day 6
3) A student is making trail mix.
A) Create a graph, using the coordinate plane below, to determine if the
quantities of nuts and fruit are proportional for each serving size listed in the
table. Label the axes and title your graph.
B) If the quantities are proportional, what is the constant of proportionality (slope/unit rate) that defines the
relationship?
C) Explain how the constant of proportionality was determined and how it relates to both the table and graph.
D) What does the point (0, 0) mean in regards to the situation?
E) What does the point (1, 2) mean in regards to the situation?
4) If Kayla can walk 2 miles is ½ an hour, what would be her unit rate per hour?
5) A car on the expressway is travelling 15 miles in .25 hours, what speed is the car travelling per hour?
Serving Size 1 2 3 4
Cups of Nuts
(x) 1 2 3 4
Cups of fruits
(y) 2 4 6 8
Using Unit Rate as a Scale Factor Classwork Day 6
6) The graph below represents the cost of a pack of gum. The unit rate is represented as $___________ each
pack. Represent the relationship using by completing the table and writing an equation of the line.
Equation _____________________________
A) Explain what each point on the graph means. B) How much will 20 packs of gum cost?
C) Explain what the point (0,0) means. D) Explain what the point (1, 0.75) means.
Number of Packs
(g)
Cost in Dollars
(d)
0
1
2
Cost
in
doll
ars
(d
)
Number of packs (g)
Lesson Summary: The points (0,0) and (1, r), where r is the unit rate, will always fall on the line representing two quantities that are proportional to
each other.
he graph.
tity.
These two points may not always be given as part of the set of data for a given real-world or mathematical situation, but they will
always fall on the line that passes through the given data points.
Using Unit Rate as a Scale Factor Homework Day 6
1) The graph to the right shows the distance (in ft.) ran by an
athlete in training.
a) What does the point (5, 280) represent in the context of the
situation?
b) What does the point (3, 168) represent in the context of the
situation?
c) Is the distance run by the athlete proportional to the time?
Explain why or why not.
d) Write an equation to represent the distance run by the athlete.
Explain or model your reasoning.
2) The following graph represents the total cost of renting a car. The cost of renting a car is a fixed amount each
day regardless of how many miles the car is driven. It does not matter how many miles you drive; you just pay
an amount per day.
a) What does the ordered pair (4, 250) represent?
b) What would be the cost to rent the car for a week? Explain or
model your reasoning.
c) What is the unit rate and what does it mean?
3) The following table shows the amount of broccoli and price
paid.
Amount of Broccoli (pounds) 2 3 5
Cost (Dollars) 1.5 2.25 3.75
a) Is the cost of broccoli proportional to the amount of broccoli?
b) Write an equation to illustrate the relationship between the amount of broccoli and the cost.
c) Using the equation, predict how much it will cost for 12 pounds of broccoli?
d) What is the maximum amount of broccoli you can buy with $11.25?
Car Rental Cost
Athlete Running Time
Dis
tan
ce
Interpreting Graphs with Proportional Relationship Classwork Day 7
Remember back on day 1 of this lesson, you were told you would be able to tell if something formed a
proportional relationship, what the constant of proportionality is, and how to graph and write an equation.
1) Hailey works for Cake Boss making brownies all
day. She can bake 6 batches of brownies in 3 hours.
a) Find the constant of proportionality.
b) Fill in the table below:
Hours(h) 0 1 4 10
Batches(b)
c) Write an equation to represent this situation.
d) Graph this situation in the graph on the right. Be
sure to label your axes for batches and for hours. Be
sure to title your graph.
d)
2) Looking to the right we have a sample question
from the state.
Last summer, a family took a trip to a beach that was
about 200 miles away from their home. The graph to
the right shows the distance driven, in miles, and the
time, in hours, taken for the trip. Show all work.
What was their average speed from hour 1 to hour 4?
a) 25 miles per hour
b) miles per hour 33 3
1
c) miles per hour 66 3
2
d) 100 miles per hour
Hours
500
450
400
350
300
250
200
150
100
50
0
Miles
Travel
3) Spencer rides his bicycle for 10 hours. He can bike
25 miles in 2 hours.
a) Find the constant of proportionality.
b) Fill in the table below:
Hours 0 1 4 10
Distance
c) Write an equation to represent this situation.
d) Graph this situation in the graph on the right. Be
sure to label your axes with miles and for hours. Be
sure to title your graph.
4) At NASA, a rocket was test fired. The graph to the
right shows the distance risen and fallen, in miles, and
the time, in minutes, taken for the trip. Show all work.
a) What was the rockets average speed from minute 0
to minute 3?
b) What happened between minute 3 through minute
6?
c) During what minutes did the rocket descend?
d) What was the rockets average rate of descent?
5) What does the points (0,0) and (1, r) represent on a
graph?
6) Define the constant of proportionality in your own
words.
150
135
120
105
90
75
60
45
30
15
0
Minutes
500
450
400
350
300
250
200
150
100
50
0
Miles
Height
Interpreting Graphs with Proportional Relationship Homework Day 7
1)
1) Explain what the point (2, 6) means in reference to the graph.
2) Explain what (0, 0) means.
3) Explain what (1, r) means where r is the unit rate.
4) This summer, Maggie would like to start saving
money. Maggie is planning on working all 10 weeks
of the summer. She saves $20 every two weeks.
a) Find the constant of proportionality.
b) Fill in the table below:
Weeks 0 1 7 10
Savings
c) Write an equation to represent this situation.
d) Graph this situation in the graph on the right. Be
sure to label your axes with weeks and savings. Be
sure to title your graph.
150
135
120
105
90
75
60
45
30
15
0
Basement Flooding
Nu
mb
er o
f In
ches
(i)
Number of Hours (h)
0
3
6
9
12
15
0 1 2 3 4
5) Fill in the blanks:
Weeks 0 1 5 10
Savings 35
6) A boy scout convention takes a road trip. There are
282 people going and only 47 cars. How many people
will need to fit in each car?
7) One day you download 4 songs for $5. Write an
equation that uses the constant of proportionality to
describe the relationships between s songs and the cost
in d dollars.
8) Last month the electric bill was $50.64 for 450
kilowatt-hours of electricity. At that rate, what would
be the cost for 240 kilowatt-hours?
9) Make up your own proportional relationship.
*Create a table *Create a graph *State the unit rate * Write situation in words
*Write an equation to represent the constant of proportionality.
Explain your situation in words.
__________________________________________________________________________________________
__________________________________________________________________________________________
Table
Graph (label axes and title)
Unit Rate/Constant/Slope ______________ Equation_________________
Unit 3 – Proportional Relationships Performance Task
1) Alex spent the summer helping out at his family’s business. He was hoping to earn enough money to
buy a new $220 gaming system by the end of the summer. Halfway through the summer, after working
for 4 weeks, he had earned $112. Alex wonders, “If I continue to work and earn money at this rate, will I
have enough money to buy the gaming system by the end of the summer?”
To check his assumption, he decided to make a table. He entered his total money earned at the end of
week 1 and his total money earned at the end of Week 4.
2) Carli’s class built some solar-powered robots. They raced the robots in the parking lot of the school.
The graphs below show the distance d, in meters, that each of three robots traveled after t seconds.
a) Each graph has a point labeled. What does the point tell you about how far that robot has
traveled?
b) Carli said that the ratio between the number of seconds each robot travels and the number of
meters it has traveled is constant. Is she correct? Explain.
c) How fast is each robot traveling? How can you see this in the graph?
3) Al’s Produce Stand sells 7 ears of corn for $1.50. Barbara’s Produce stand sells 13 ears of corn for
$2.75. Write two equations, one for each produce stand that models the relationship between the number
of ears of corn sold and the cost. Then use each equation to help complete the tables below.
4) During their last workout, Izzy ran 2 ¼ miles in 15 minutes and her friend Julia ran 3 ¾ miles in 25
minutes. Each girl thought she were the faster runner. Based on their last run, which girl is correct?
Show all work.
5) Championship T-shirts sell for $22 each.
a. What point(s) MUST be on the graph for the quantities to be proportional to each other?
b. What does the ordered pair (5, 110) represent in the context of this problem?
c. How many T-shirts were sold if you spent a total of $88?