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


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?


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


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


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


(c) = _____

Equation______________

Hours (h) 2 10 16

Pay (p) $11 $55 $88

3)


(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


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


y

Write the equation that satisfies this graph.


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.


y

x

y

x

= c,

Then write your equation as

y = ___ x

Constant/slope

__________

Equation

____________

Constant/slope

__________

Equation

____________



y

Write the equation that satisfies this table.

x y

0 0

1 3

2 6

3 9


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

# of rooms

painted (p)

1.5 7.5 18 30



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


(k) = _____

Equation___________________

Days

(d) 5 10 15

Wages

(w) $51.25 $102.50 $153.75

2) price per pound


(k) = _____

Equation___________________

Pounds 4 5 6

Price $7.96 $9.95 $11.94

3) pounds per bag


(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 ________________


Equation ________________


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?


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


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.



Hours 0 1 4 10

Distance



sure to label your axes with miles and for hours. Be


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

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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.



Weeks 0 1 7 10

Savings



sure to label your axes with weeks and savings. Be


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Basement Flooding

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(i)

Number of Hours (h)

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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?

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Proportional Relationships - Ms. Schmidt's Math Class

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