1

Unit 5

Interpreting

Graphs

NAME:______________________ GRADE:_____________________ TEACHER: Ms. Schmidt _

2

Proportional Linear Functions Classwork Day 1

Proportional linear functions can be written in the form y = mx, where m ≠ 0

**The y-intercept (b) is always 0 – which means the line will pass through the origin!!

Example: y = 5x is a proportional relationship because it is in the form of y = mx

Direct Proportion is m or slope of the line. It is also called the constant of proportionality OR constant of

variation. It also represents the unit rate.

Example: y = 5x

The direct proportion is_____________, ___________________, _________________, _________________

The constant of proportionality is ______________, _________________, _____________, _____________

The initial value is__________,

All proportional functions pass through the________________

Complete the table for a – c

A. y = 4x

B. xy5

3

C. y = x

Non-proportional linear functions can be written in the form y = mx + b

1) Which equations represent a proportional relationship?

a) y = 3x + 4 b) y = x c) y = ½ x d) y = x2 e) y = -2x – 8 f) y = 1

3𝑥

2) Which equations represent a proportional linear function?

A) y = 3x + 6 B) y = ½ x – 3 C) y = 7x D) y = -2x – 4 E) y = 2

3 x

3) What is the direct proportion for each proportional linear function?

A) y = 4x B) y = 3

5x C) y = x

Slope A B C

Constant of Variation A B C

Unit Rate A B C

Constant of Proportionality A B C

3

Proportional Linear Functions Classwork Day 1

4. Compare the two graphs:

What is the slope of line A? What is the slope of line B?

What is the constant of proportionality?

What is the equation of the line? What is the equation of the line?

Which graph represents a proportional relationship? Justify your reasoning.

5. The graph represents the distance a car can travel based on the number of gallons of gas.

A. Is it proportional?

B. Find the unit rate.

C. Write the equation.

Tell whether each graph is proportional.

6) 7)

Sod Sales

Area (sq. ft)

Tota

l Co

st

($

)

Mowing Lawns

Lawns

Profit

($)

4

Proportional Linear Functions Classwork Day 1 Determine whether each table is proportional. If so, state the constant of proportionality.

8) 9)

10)

Find the constant of proportionality for each table or graph and write the equation.

11) yards of cloth per blanket

Yards (y) 16 32 40

Blankets (b) 8 16 20

12) pay per hour

Hours (h) 2 10 16

Pay (p) $11 $55 $88

13) profit per shirt sold

Shirts (s) 5 10 15

Profit (p) $7.50 $15.00 $22.50

14) 15)

16) The table shows the total number of text messages that Brad sent over 4 days.

a) Write an equation to find the total number of messages sent in any number of days. Describe the

relationship in words.

__________________________________________________________________________________________

__________________________________________________________________________________________

___________________________________________________

b) Use the equation to find how many text messages Brad would send in 30 days.

x 2 4 6 8 10

y 1.5 3 4.5 6 7.5 x 1 2 4 7 9

y 5 9 17 29 37

x 1 2 3 4 5

y 2 8 16 32 64

Number of Days, d 1 2 3 4

Total Messages, m 50 100 150 200

Hours

Mile

s

5

Proportional Linear Functions Homework Day 1

Find the constant of proportionality and write an equation.

1) wages per day

Days

(d) 5 10 15

Wages

(w) $51.25 $102.50 $153.75

2) price per pound

Apples

(a) 4 5 6

Price

(p) $7.96 $9.95 $11.94

3) pounds per bag

Bags (b) 3 8 11

Dog

Food (lb)

(d)

7.5 20 27.5

4) 5)

6) Determine whether the linear function is a proportional function, if so state the direct

proportion.

7) Each graph shows the rate of change by four different landscapers for a landscaping job. Which graph

shows a proportional relationship?

x 1 2 3 4

y 350 700 1050 1400

Tickets (t)

Dance Tickets

Pro

fit

(p

)

Oranges (f)

Fruit Price per

Pri

ce (p

)

6

Proportional Linear Functions Homework Day 1

8) Which table represents a proportional relationship?

9) Which of the following tables represents a proportional relationship?

A. B. C. D.

10) Which of the following graphs represent a proportional linear function?

A B C D

11) Write an equation whose direct proportion is 2

5 . _______________________

12) Which is the equation of a line that intersects the y-axis at 2 and has a slope of -2?

A) y = 2x – 2 B) y = -2 + 2 C) 2y = -2x + 2 D) y = -2x + 2

13) What is the value of (23)-2?

A) 0 B) 1

16 C)

1

8 D) 1

14) A right whale eats an average of 2 tons of plankton every day. The relationship between the number of

days and the tons of plankton eaten is given by the table and the graph. What is the constant of variation?

2 4 6

1 2 4 2 4 6

4 5 6

2 4 6

3 5 7

2 4 6

5 10 15

7

Interpreting Graphs Classwork Day 2

Vocabulary:

Interpret: __________________________________________________

1. A locksmith charges a flat fee for each house call plus an hourly rate, as shown by the graph below.

a) What does the x-axis represent?

b) What does the y-axis represent?

c) What does the rate of change represent?

d) What is the rate of change?

e) What is the flat fee that the locksmith charges?

f) What equation can we use to find how much an 8 hour job is going to

cost?

2. A shoe store offers free points when you sign up for their rewards cards. Then, for each pair of shoes

purchased, you earn an additional number of points. The graph shows the total point earned for several pairs of

shoes. a) Interpret the rate of change and the initial value.

b) Find the rate of change

c) Interpret the initial value

d) Find the initial value

e) Write the equation used to represent the situation.

f) What does the point (4,90) represent?

8

Interpreting Graphs Classwork Day 2

3. The table shows how much money Tori has saved. Assume the relationship between the two quantities is

linear.

a) Interpret the rate of change

b) Find the rate of change

c) Find the initial value

d) Interpret the initial value

e) Write the equation that model this situation

4) a) What does the slope represent?

b) Write the equation to represent the situation.

c) Does the graph represent a proportional relationship?

Number of

Months, x

3 4 5 6

Money Saved,

y

110 130 150 170

9

Interpreting Graphs Homework Day 2

1. Ms. Pickford rides her bike at a steady rate away from her house. Her distance from the house over time is

shown below. How fast is Mrs. DiGiacinto riding?

2. Sirius Radio charges a yearly subscription fee plus a monthly fee. The total cost for different numbers of

months, including the yearly fee, is shown in the graph. Find and interpret the rate of change and the initial

value.

3. Joanie bought an airplane phone card that charges her a connection fee plus an additional rate for each

minute the call lasts.

a) What does the slope of the line represent?

b) What is the slope of the line?

c) What does the initial value represent?

d) Write an equation that can be used to determine the cost of a

call on the airplane?

e) If Joanie talks to her mom for 20 minutes, how much will

the call cost?

10

Interpreting Graphs Homework Day 2

4. An airplane ascends from an altitude of 14,000 to an altitude of 20,000 feet in 15 minutes. Its altitude over

time is shown in the graph below. Calculate and interpret the rate of change of the plane’s altitude with respect

to time.

5. Simplify the expression 55 ∙ 5-7

A) 512 B) 52 C) 1

52 D) 1

512

6. Which expression is equal to13−11

13−12?

A) 13-23 B) 13-1 C) 13 D) 13132

7. Which ordered pair represents a point that would lie on the graph of y = 4x – 10?

A) (4, -10) B) (4, 6) C) (-4, 6) D) (-4, 10)

8. The Grade 8 class is planning a party. The graph shows refreshments costs , y, based on the number of

students who will attend the party, x. What is the equation of the graph in slope-intercept form?

A. y = 0.4x + 10

B. y = 2.5x + 10

C. y = 3x + 10

D. y = 10x + 2.5

11

Interpreting Graphs Classwork Day 3

1) The table shows the distance, y, in meters, that Ariel can run during the time, x, in minutes.

What does the slope of this line represent?

What is the rate of change?

Does the table show a direct proportion?

2) The following table represents the conversion from quarts to liters.

A. What is the rate of change?

B. Write an equation to find the number of liters in any number of quarts.

C. How many liters are in 8 quarts? D. Does this represent a direct proportion? Justify your answer.

3) a) What is the rate of change?

b) Write an equation to find the number

of miles run y after any number of days s.

c) How many miles will Marion run in the

month of September

Quarts, q Liters ,l

1 0.95

2 1.9

3 2.85

4 3.8

5 4.75

12

Interpreting Graphs Classwork Day 3

4. Use the graph to the right to answer the following questions.

a) Which sections of the graph are:

Increasing

Constant

Decreasing

b) What was the total change in income from the beginning of March

through the end of April?

c) What was the total change in income from the beginning of March

through the end of May?

5) The graph represents the number of people in an outdoor stadium for a baseball game.

a) What do the x- and y-axes represent?

b) Explain what could be happening during each

section of the graph,

c) How could a graph such as this be valuable to the

owners of the baseball team? Explain.

6. Enrique is taking a plane trip. The plane will take off and ascend for about 20 minutes, maintain a constant

attitude for about 50 minutes, and then descend for about 20 minutes before landing. Which graph shows

Enrique’s trip?

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Interpreting Graphs Classwork Day 3

7. Create a situation the graph could represent: 8. Wendy draws the graph below to represent a situation.

Which statement correctly interprets the graph?

A. Wendy’s cup collection is decreasing over time.

B. Wendy’s cup collection is increasing at a rate of

10 cups per month

C. Wendy’s cup collection is increasing at a rate of

5 cups per month

D. Wendy’s cup collection is increasing at a rate of

1 cup every two months

9. Michelle and Adam pay their babysitter $2 an hour to baby sit their child. Which graph correctly shows the

relationship between the number of hours the babysitter works, x, and the total cost in dollars, y?

10. Which table represents a proportional relationship?

A. B. C. D.

11. A. What does the slope represent? Car Trip

B. Write the equation to represent the situation.

C. Does the graph represent a direction proportion?

14

Interpreting Graphs Classwork Day 3

12. John drew the graph below to represent a situation.

Which statement could describe the situation John graphed?

A. The temperature of a TV dinner cooking in a microwave increases 100° every minute.

B. The temperature of a TV dinner cooking in a microwave increases 20° each minute.

C. The temperature of a TV dinner cooking in a microwave decreases 15° each minute.

D. The temperature of a TV dinner cooking in a microwave decreases 20° each minute.

13. Match the graph to the description: a) A car starts from a complete stop and accelerates at a

constant rate. Then it travels at a constant speed unit the driver

sees a stop sign and gradually slows down to a stop.

b) A car is traveling at a constant speed. It accelerates at a

constant rate. Finally, it continues traveling at a constant speed.

c) A car slows down at a constant speed as is approaches a

red light. After a short time, the light changes and the car

gradually accelerates.

14. Describe a situation that can represent the given graph.

15

Comparing Rates of Change & Graphs Classwork Day 4

Which of the graphs is the steepest?

A. Greater Rate of Change – the higher the absolute-value of the slope, the steeper the line.

1. Which equation has a greater rate of change?

A) y = 2

5𝑥 + 5 B) y = 2x + 5 C) y = -3x + 9

2. Which of the following has the greater rate of change?

A) 3x + 4y = 8 B) (3,6) and (4,9) C) D)

3. Make a valid statement comparing the equation y = -2x + 6 and the graph below. Use facts to support

your statement.

x Y

6 10

7 15

8 20

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Comparing Rates of Change & Graphs Classwork Day 4

4. Two airplanes leave an airport and travel at a steady speeds. The first plane’s distance from the airport in

miles, d, over time in minutes, t, is given by the equation below.

First airplane: d = 4.9t

The second plane’s distance from the airport over time is given by the graph.

Find the speed of each airplane with the proper units.

First Airplane: ___________________

Second Airplane: ______________

Which plane travels at the faster rate, and by how much?

____________________________________________________________________________

5. Tom and Eric are both house painter, and each charges an hourly rate of a painting job. The equation

y = 13x shows the total charge, y, in dollars, for hiring Tom to paint a house for x hours. The table below shows

the same information for Eric.

Eric’s Charges

Which statement is true?

A) Tom’s hourly rate is $1.00 cheaper.

B) Eric’s hourly rate is $1.00 cheaper.

C) Eric’s hourly rate is $13.00 cheaper.

D) Tom and Eric work for the same hourly rate.

6. The number of new movies a store receives can be represented by the function m = 7w + 2, where m

represents the number of movies and w represents the number of weeks. The number of games the same store

receives is shown in the table.

a) Compare the functions’ y-intercepts and rates of change.

____________________________________________________________________________________

__________________________________________________________

b) How many new movies and games will the store have in 6 weeks?__________________

x 2 4 6 8

y 26 52 78 104

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Comparing Rates of Change & Graphs Homework Day 4

1) The population of two small towns change at a steady rate over a 10-year period. The population of

Holbrook is given by the equation below, where P is the population, and t is the number of years since the year

2000.

Population of Holbrook: P = -40t + 920

The population of Easton is shown in the graph.

Find the rate of change in each town’s population with the proper units

Holbrook: ________________

Easton: ________________

Make a valid comparison based on the given information.

_____________________________________________________________________________

2. Renee and Alissa each have a monthly cell phone bill. Renee’s monthly cell phone bill is represented by the

function y = 0.15x + 49, where x represents the minutes and y represents the cost. Alissa’s monthly cost is

shown in the graph.

a) What does the 49 represent in Renee’s function?

b) What does 60 represent in Alissa’s graph?

c) Compare the y-intercepts and the rates of change.

d) What will be the monthly cost for Renee and Alissa for 200 minutes?

18

Comparing Rates of Change & Graphs Homework Day 4

3. Darielle’s mother needs to rent a truck to move some of her antique furniture. The cost to rent a truck from

two different companies is show in the table and graph. Which company should she use to rent the truck for 40

miles?

4. Sean and Ryan each have a membership to the gym. Sean’s membership is represents by the function

y = 3x + 29, where x represents the hours with a trainer, and y represents the cost. The cost of Ryan’s

membership is shown in the graph.

a) Compare the y-intercepts and rate of change.

b) What will be the total cost for Sean and Ryan is they each have 4 hours with a

trainer?

5. Cassie has to buy several pounds of tomatoes at the farmer’s market. The graph shows the cost of buying

tomatoes at Farms Stand 1. The equation y = 4x gives the cost of buying x pounds of tomatoes at Farm Stand 2.

Which farm stand offers the better price?

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Representing a Function Classwork Day 5

Every function can be written 4 ways:

1 - ___Equation__________________

2 - ___Graph____________________

3 - ___Table_____________________

4 - ___Word Problem______________

Create a function rule (equation) to represent each situation

7) A) Write the equation B) Make a table from the line

of the line

C) Create a situation to represent this graph

1) Emma is writing a term paper.

She writes 3 pages per day. If y

represents the total pages and x

represent days, create a function

rule for this scenario.

2) A large pool contains 20,000

gallons of water. 5 gallons

evaporate each day. y is the

gallons of water and x is the days.

Write an equation.

3) In a bank account Joe has $45.

He earns $2 per day. Write an

equation for the situation.

4) You sell candy for a school fundraiser. You sell

each box for $3. Write an equation for this scenario.

5) Mr. Murphy has been working out. His bicep started

out at 10”. If he gains ½” per month, write an equation

to match this situation.

6) You open up a lemon-aide stand. You sell 13 lemon-aides per hour (x). Write an equation for this situation.

x y

20

Representing a Function Classwork Day 5

8) y = -2x + 4

A) Make a Table B) Graph the line

C) Write a situation to model table.

9) Amy has $10 in her piggy bank. She spends $1 per day on ice cream.

A) Write an equation B) Make a Table C) Graph the line

10) A student trying to save the Holtsville Ecology site was getting signatures on a petition. Matyson already has 120

signature and want to continue at a rate of 30 signatures a day.

a) What does the 120 represent?

b) What does the 30 represent?

c) Write the equation to model this situation

11. Write a situation that represents the function y = 55 - 8x.

x y

x y

21

Representing a Function Homework Day 5

1. A caterer charges $120 to cater a party for 15 people and $200 for 25 people. Assume that the cost, y, is a

linear function of the number of x people.

a) Write an equation in slope-intercept form for this function.

b) What does the slope represent?

c) How much would a party for 40 people cost?

2. An attorney charges a fixed fee on $250 for an initial meeting and $150 per hour for all hours worked after

that.

a) Write an equation to represent the attorney’s total charges.

b) Find the charge for 26 hours of work.

3. A video rental store charges a $20 membership fee and $3 for each video rented.

A) Write an equation B) Make a Table C) Graph the line

4. Which of the following is linear?

A) y = 3x2+ 4 B) y = x3 C) 2x + y = 6 D)y = x1/2

x y

22

Representing a Function Homework Day 5

5) A) Write the equation B) Graph the line

(function rule) of the line

C) Write a situation to model table.

6) A taxi company charges its customers according to the equation C = 1.2x + 1.5, where C is the cost of the

ride in dollars and x is the length of the ride in miles.

a) What does the 1.2 represent in this situation?

b) What does the 1.5 represent?

c) What happens to the cost of the ride as the amount of miles increase?

d) What will the cost of a 30 mile ride be?

7) Jimmy makes $8.50 per hour. Write an equation that shows how much Jimmy makes, y, based on the

number of hours he works, x.

8) Disney World charges a rental fee plus $2 per hour for strollers. The total cost of 5 hours is $13. Assume

the relationship is linear. Find and interpret the rate of change and initial value.

x y

2 -6

4 -2

6 2

8 6

23

Scatter Plots Classwork Day 6

Scatter plot is a graph used to show relationship that exists between the data.

1) The owner of a diner wanted to find out if outside temperature affects soup sales. Create a scatter plot from

the table below.

a) Plot the data points on the above coordinate grid.

Use a consistent and appropriate scale.

b) Does the graph represent a linear function? Explain.

c) What conclusion can you make based on the graph?

d) Outliers - _______________________________

_________________________________________

_________________________________________

B. Correlation - A scatter plot can show that a relationship exists between two sets of data.

Temperature (in F) 30 32 35 40 40 45 54 60 64 68

Bowls of Soup Sold 8 50 42 42 38 28 22 15 16 5

24

Scatter Plots Classwork Day 6

For each scatterplot, tell whether the association (correlation) (relationship) is positive, negative, or no

association.

1) 2) 3)

25

Scatter Plots Classwork Day 6

6. Christina works at the ice cream shop during summer vacation. She uses the following table to record the

highest temperature each day for two weeks and the number of ice cream cones she sold on each of those days.

a) Use the graph to the right to

create a scatter plot of the data.

b) What type of correlation does

the graph represent?

c) Are there any outliers in the data?

If so, what are the ordered pairs of the points?

7. Which graph could represent the relationship between the time, in minutes, water in a pot is heating, x, and

the temperature of the water, y, if the beginning temperature of the water is 0 degrees and once the temperature

gets to 100 degrees it remains at that temperature?

8. A tiger in captivity is fed 13.5 pounds of food a day.

The graph shows the pounds of food an elephant in captivity eats per day.

a) Write a function to represent the food consumed by

a tiger in captivity.

b) Compare and contrast the food consumption of a tiger

and an elephant in captivity.

26

Scatter Plots Classwork Day 6

9. The scatter plot below could represent the relationship:

A. between length of hair and the length of fingernails

B. between inches of monthly snowfall and the number of sunny days

C. between a student’s distance from school and the time it takes her

to get to school

D. between hours spent studying and the number of incorrect answers

on a test

10. What is the slope of the line?

A. -4

B. 4

C.

D.

11. Alisha needs to graph y = -2x + 1. So far, she has plotted (0, 1) as shown below. Which is the next

point Alisha could plot?

A) (1, -1)

B) (1, 3)

C) (2, 0)

D) (2, 2)

27

Trend Line/Line of Best Fit Classwork Day 7

Trend Line/Line of Best Fit - A line drawn on a scatter plot close to most of the data points. It can be used to

estimate data on a graph

1)

g) Interpret the slope of the line of best fit. ______________________________________________________

2) Lucia ships eight packages from a delivery company. She then creates a scatter plot of her data and draws a

trend line through the data points.

A) What is the equation of the trend line drawn?

______________________

B) Interpret the slope of line of best fit _______________

_________________________________________

_______________________________________________

C) Based on this trend, what is the cost of 60 lbs?

___________________________

D) If the cost is $40, what is the shipment weight?

___________________________

Savings vs. Years

Years

Savings in

Bank

Account

In Thousand

$

a) Draw a trend line for the data.

b) Does the trend line show a negative, positive, or

no correlation? ________________________

c) Does the trend line show a linear association or

a nonlinear association? __________________

d) What information do we need in order to

determine the equation for the trend line?

________________________________

e) What is the equation of the line of best fit?

______________________________________

f) Name one outlier _________________

28

Trend Line/Line of Best Fit Classwork Day 7

3) Joey kept track of the number of free throws that his team shot in a practice and the percentage that they

made in the next game. He displayed his finding in the scatter plot shown below.

a) Draw a trend line for Joey’s data.

b) What is the correlation?

c) Does the trend line show a linear or a nonlinear association?

d) What is the equation of the line of best fit?

e) A student takes 60 free throws during practice. Using the

equation for the line of best fit, find the free throw percentage

that the student is likely to have during the next game.

4. The following scatter plot shows the prices and 5. What is the equation for the line of best fit?

weights of several pieces of Amanda’s jewelry,

as well as a trend line that shows their relationship.

a) Interpret the slope

b) Interpret the y-intercept

c) Write the equation of the line

29

Trend Line/Line of Best Fit Classwork Day 7

7. The owner of a diner wanted to find out if outside temperature affects soup sales. The scatter plot show a

sample of data that the owner collected.

a) Is there an association between

the outside temperature and soup sales?

If so, is it positive or negative?

b) Draw the line of best fit.

8. The scatter plot shows a plumber’s charges and the time 3. For the graph below, draw the trend line and

he spends at each job, as well as the trend line. What is the write the equation for the line of best fit.

equation of the trend line?

9. Consider the pair of identical scatter plots. Which plot shows the better trend line? Explain.

30

Trend Line/Line of Best Fit Classwork Day 7

10. Use the plot to the right:

a) Draw a trend line

b) What is the y-intercept of the trend line?

c) Explain what the y-intercept of the trend line represents.

d) What is the slope of the trend line?

e) What is the equation of the trend line?

Use the following graph to answer questions 11 and 12.

11. What is the y-intercept of the graph?

A. -1.5 B. 2 C. 3 D. 0

12. What is the equation of the line?

A. y = 2x + 3 C. y = 3x + 3

B. y = -2x + 3 D. y = -3x + 3

13. What is the equation 2x + y = 9 written in slope/y-intercept form?

14. What is the solution to 12 – 12n = -24?

A) n = 5 B) n = 3 C) n = -3 D) n = -5

10) Kara used the linear model y = 20,000 + 0.3x to predict her total salary from achieving total sales of x. What is her

base salary?