DEPENDENT AND INDEPENDENT - North Thurston … and Independent 3 Activity 1: Function I. Read each numbered statement. Determine the two variables (in words) in each situation and

Dependent and Independent 1

DEPENDENT AND INDEPENDENT

Enduring Understanding: Develop a better understanding that using systems of equations in

graphical form is appropriate to determine a solution. Develop a better understanding of how to use

variables to write linear equations. Develop a better understanding of how to write an equation and

then substitute values in the equation to answer a question. Develop a better understanding of

identifying or writing a rule to describe a linear function. Develop a better understanding of drawing

conclusions and supporting them.

Essential Questions:

What is meant by the terms “dependent variable” and “independent variable”?

Science uses “responding” and “manipulated” instead of “dependent and “independent”.

How can we use all terms without confusion?

How do the dependent variable and independent variable relate to graphing?

What is meant by the term “function”?

How do you know when points on a graph represent a function?

How is an algebraic equation developed from information provided?

What do the variables represent in an equation? How are the variables replaced in order to

reach a solution?

How information is converted to coordinates and placed on a coordinate grid?

How are coordinates written and then turned into a symbolic representation?

What is an informative title for a graph?

What are appropriate intervals for the x- and y-axes?

What do the intercepts of a graph represent in the context of a given situation?

What does the slope of a graph represent in the context of this scenario?

How can a graph be used to make predictions?

What is meant when two lines in a graph intersect?

How can a conclusion be supported using mathematical information and calculations?

How can I use a calculator to assist in the solving of a problem through graphing?

How do I choose a window for the calculator when graphing?

What does the window do to help me when graphing?

Length of the Lesson: 450 minutes; an additional 250 minutes for optional activities

Lesson Overview:

Before allowing the students the opportunity to start the activity 16: access their prior

knowledge with regards to joining a health club. Why would a person join one club vs.

another? Is cost the only factor? Spending dollars vs. saving dollars? Ask the students if any

of them belong to a health club. What do they like about the health club? Discuss why more

and more companies, apartment complexes, hotels and colleges have good fitness centers.

Why do these places include fitness centers? What is the benefit of including a fitness center

in these places?

There are several ways that a function can be written as a statement. Be sure to address a

variety of possibilities. These include but are not limited to using terms such as; depends,

determines, hinges on, establishes, decides, causes and effects.

Important concepts are identifying the two quantities involved and determining the dependent


and independent relationships. Many times, parts of this statement can be interchanged. For

example, if discussing gas in a car and the amount of money you have, either statement of a

function is accurate but the dependency changes:

The amount of money I have after I put gas in my car depends on how much gas I put

in my car.

How much gas I put in my car depends on how much money I have.

Discuss with students that sometimes the situation above exists; however, the question

statement will help decide the dependency. Don‟t let this become an issue that distracts

students from the concept of independent and dependent quantities.

In Activity 1, many of these statements could be turned around and the dependent statement

could become the independent. Students may point out that the number of hours they work

depends on how much money they need to make. The idea here is to associate independent

and dependent quantities with specific statements and words such as depends, determines,

and function. As the statements are written, the dependency is established. Allow and

encourage students to discuss how changing the dependent or independent statement affects

the other.

Explain what moving toward/away from motion detector means.

Activities 4-6 may need additional scaffolding regarding slope and y = mx + b dependent

upon the needs of the students.

How can you support a conclusion that you make? What evidence from graphs can be used

to support/justify your conclusion?

A good warm-up could be Payday or Tall Paul.

When reading a graph, where are the x- and y-intercepts? What is the relationship between

the intercepts and the context of any problem?

Activities 13, 14 and 15 are graphing calculator-based units that are included in this overall

lesson, but are viewed as optional.

Use resources from your building.

Materials: Motion Detector

Graph paper

Graphing Calculators

Rulers

Colored pencils

EALRs/GLEs:

1.5.1-- Apply knowledge of patterns or sequences to represent linear functions

1.5.2-- Determine an equation or rule for a linear function represented in a pattern, table, graph, or

model.

1.5.4-- Use variables to write expressions, linear equations and inequalities that represent situations

involving rational numbers, whole number powers, and square roots.

1.5.6-- Apply properties to solve multi-step equations and systems of equations.

3.2.1-- Draw and support conclusions, using inductive or deductive reasoning.

Item Specifications: AS01; AS02; AS03; SR04

Assessment: Use the multiple choice and short answer items from Algebraic Sense and Number

Sense that are included in the CD. They can be used as formative and/or summative assessments

attached to this lesson or later when the students are being given an overall summative assessment.


Activity 1: Function

I. Read each numbered statement. Determine the two variables (in words) in each situation and

identify each as independent or dependent.

a. Independent (Manipulated) variable – Not subject to control by others, self-governing. The

independent variable is usually associated with the horizontal, or x axis. A common example of

something not subject to the control of others, would be time, in the form of minutes, hours, days,

etc. The independent variable is also referred to as the “input”. Another way of thinking of the

independent variable is it is “free” and not dependent on some other action. For instance if I drop

a ball off a building, the time required for the ball to hit the ground is “free” and is not in the least

affected by the height of the building, me, the ball, or anything else. Thus in this case time is

independent of the height of the ball (distance above the ground).

b. Dependent (Responding) variable – Relying on or subject to something else for support. The

dependent variable is usually associated with the vertical, or y axis. It‟s sometimes easier to figure

out the dependent variable first, because we can see when something is relying on something else

for support. Such as in our example above, time is not dependent on height, but the ball‟s distance

above the ground is dependent on the time it was dropped.

1. How fast the grass grows depends on how much rain we get.

a. Independent variable how much rain________________________________________________

b. Dependent variable – how fast the grass grows________________________________________

2. The number of problems missed on a test determines your grade on the test.

a. Independent variable -_____________________________________________________________

b. Dependent variable - ______________________________________________________________

3. How long I talk on my cell phone depends on the number of minutes on my calling plan.



4. The amount of money I make is a function of the number of hours I work.



5. The number of cakes sold in a bake sale determines the amount of money made.




6. The winner of the football game depends on which side scored the most points.



7. The amount of memory on a CD determines how many songs I can download to it.



II. The American Heritage Dictionary defines function as something closely related to another thing

and dependent upon it for its existence, value, or significance. The words function and depends can

be used interchangeably.

Examples of Function – Write sentences that represent a function. Determine the independent

and dependent parts. Include several different words such as depends, determines, and „is a

function of‟ in your statements.

1. How much money I make depends on the number of hours I work

a. I control the hours I work – independent variable

b. The money depends on the hours – dependent variable

2. _______________________________________________________________________________



3. _______________________________________________________________________________



4. _______________________________________________________________________________



5. _______________________________________________________________________________




6. _______________________________________________________________________________



III. Identify the cause and effect variables from the dependent functions you created in numbers 2-6.

Cause

Effect


Activity 2: Exploring Dependent and Independent

1. Mathematics is considered a universal language. People from all parts of the world read and

interpret mathematical statements the same way. In order for this to happen, universally accepted

mathematical terms, words, and symbols were established and defined. We call these “conventions”.

Order of operations is one of these conventions. Worldwide, all people agree that problems will be

simplified using the order of operations you have learned. Another convention is the agreement that

the x-axis will represent the independent (manipulated) variable and the y-axis will represent the

dependent (responding) variable. Applying this agreement, determine the independent and dependent

quantities of each statement and label the axes on the graph.

a. My grade in Algebra depends on how long I study.

b. The longer I procrastinate, the less amount of work I

accomplish.

c. The number of CDs I buy depends on how much money

I have.

d. The cost of the taxi ride is a function of the number of

miles I ride.


Activity 3: Dependent (Responding) Stories

1. Use the axes‟ labels to write a dependent (responding) statement.

Example: Statement: How far I walk is dependent on how long I

walk

_______________________________________

a.

Statement: ___________________________________

_____________________________________________

_____________________________________________

_____________________________________________

_____________________________________________

b.

Statement: ___________________________________

____________________________________________

____________________________________________

____________________________________________

____________________________________________


Activity 4: Describe the Walk

1. Sketch and label the graph and units in the table. Write a description of the walk or run and an

equation. Include the units of measure in the table that you decide upon.

a. Verbal Description: ________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

b. Equation: ____________________________________________________________




___________________________________________________________________________

___________________________________________________________________________

b. Equation: ____________________________________________________________





___________________________________________________________________________

___________________________________________________________________________

b. Equation: ____________________________________________________________




___________________________________________________________________________

___________________________________________________________________________

b. Equation: ____________________________________________________________


Activity 5: Wandering Around

1. Label the table and graph. Fill in the table, sketch the graph and write an equation for the

situation.

a. Ryan was walking away from the motion detector at 2 feet per second. You missed where

he started, but you know that he was at the 9 foot mark after walking for 3 seconds.

Equation (equation of the line): ____________________________________________

b. How does the equation relate to the original problem? _________________________

___________________________________________________________________________

2. Madeline was walking toward the motion detector at 3 feet per second. You missed where she

started, but you know that she was at the 9 foot mark after walking for 2 seconds.

a. Equation (equation of the line): __________________________________________


___________________________________________________________________________


3. Robyn started 1 foot from the motion detector. You looked up and she was at 5 feet at the 2nd

second.



___________________________________________________________________________

4. You looked up and Chet was walking toward the motion detector. He was at the 6 foot mark at

the 1st second and the 1 foot mark at the 2

nd second



___________________________________________________________________________

Table

Time (Sec) Distance (ft)


Activity 6: Guess My Function!

Write an equation that represents the relationship between x and y in each table:

1. 2.

1. _______________________________________________________________________________

2. _______________________________________________________________________________

3. _______________________________________________________________________________

4. _______________________________________________________________________________

5. _______________________________________________________________________________

6. _______________________________________________________________________________

x y

0 1.3

1 2.5

2 3.7

x y

0 11

1 16

2 21


7. _______________________________________________________________________________

8. _______________________________________________________________________________

9. _______________________________________________________________________________

10. ______________________________________________________________________________

11. ______________________________________________________________________________

12. ______________________________________________________________________________

13. ______________________________________________________________________________

14. ______________________________________________________________________________


Activity 7: Mathematical Definitions of Functions

1. Look at the scatter plots. List the coordinate points, connect the points from left to right, and

decide if the data represents a function based on the definition of a function. The definition of a

function is for each independent value there is only one dependent value.

Coordinates: _________________________ Coordinates: ________________________

_____________________________________ ____________________________________

Yes or No _______________ Yes or No ______________

Coordinates: _________________________ Coordinates: _______________________

_____________________________________ ___________________________________

Yes or No _______________ Yes or No ______________


Coordinates: _________________________ Coordinates: _________________________

_____________________________________ _____________________________________

Yes or No _______________ Yes or No ______________

2. What do the coordinates tell you about whether the data represents a function? Make a conclusion

about what a graph looks like when it follows the definition of a function. Support your conclusion

using an example or other evidence from this lesson.

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________


Activity 8: Coordinate Points

1. Using each of the lists of coordinate points: create a table of values and a scatter plot for each

group of coordinates. Explain which groups of coordinate points follow the definition of a function.

a. (-1, -2); (3, 3); (-3, 6); (0, -3); (5, 1)

Does this group of coordinate points represent a function? _____________

Why? ____________________________________________________________________

__________________________________________________________________________

__________________________________________________________________________

b. (-4, 9); (-2, 5); (1, -1); (-2, 7); (4, -3)

Does this group of coordinate points follow the definition of a function? _____________

Why? __________________________________________________________________

________________________________________________________________________

______________________________________________________________

X Y

X Y


c. (-1, -5); (2, -5); (4, -5); (-5, 2); (-3, 3)


Why? ____________________________________________________________________

__________________________________________________________________________

__________________________________________________________________________

d. (-3, 5); (-1, -1); (1, -1); (2, -7); (-3, -5)


Why? ____________________________________________________________________

__________________________________________________________________________

__________________________________________________________________________

X Y

X Y


Activity 9: What’s the Situation?

1. Read each of the following situations and determine whether it represents a function.

Justify your answer.

Example: The ages of the students in this classroom matched to their shoe size. _________________

No, this is not a functional situation. Different aged students may have the same shoe size.________

_________________________________________________________________________________

_________________________________________________________________________________

a. The numbers on a telephone depend on the letters on the phone. ____________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

b. The letters on the telephone depend on the numbers on the phone. ___________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

c. The number of days in a month depends on the month. ____________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

d. The cost of renting a car if there is a charge of $0.50 per mile. ______________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

e. The number of minutes used on a cell phone in January depends on the students in this class.

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________


Activity 10: Valentine’s Day Idea

The school‟s drill team has contacted several flower distributors and has narrowed the choice to two

companies.

Option 1: Roses-R-Red has offered to sell its roses for a fixed down payment of $20.00 and an

additional charge of $0.75 per stem.

Option 2: The Flower Power has offered to sell its roses for a fixed down payment of $60.00 and

an additional charge of $0.50 per stem.

1. Predict which offer is the better deal. _______________________________________________

Explain why you made your choice: __________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________


2. From the description of the two offers, complete the chart to find an algebraic rule that will

determine the cost of n roses.

Rose Offers

Number of Roses

Process

Column

(Roses-R-Red)

Cost at

Roses-R-Red

Process

Column

(Flower Power)

Cost at

Flower Power

10 20 + 10(0.75) $27.50 60 + 10(0.50) $65.00

20

40

60

120

150

210

240

1,000

n

a. Write a rule for the cost of roses at Roses-R-Red using words and symbols.

1) Sentence using words: _____________________________________________________

_________________________________________________________________________________

2) Sentence using symbols: ___________________________________________________

_________________________________________________________________________________

b. Write a rule for the cost of roses at Flower Power using words and symbols.

1) Sentence using words: _____________________________________________________

_________________________________________________________________________________

2) Sentence using symbols: ___________________________________________________

_________________________________________________________________________________


c. What patterns do you observe from the table of values? _______________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

d. What happens to the cost of the roses as the number of roses purchased increases? _________

_________________________________________________________________________________

_________________________________________________________________________________

e. What would a graph of this relationship look like? ___________________________________

_________________________________________________________________________________

_________________________________________________________________________________

f. How many roses can you buy from Roses-R-Red for $65.00? __________________________

Support your answer using words, numbers and/or diagrams.

g. How many roses can you buy from Flower Power for $65.00? _________________________


h. What is the point where the two flower dealers charge the same amount? ___________

i. Write an equation that represents the point where the two flower shops charge the same

amount. _________________________________________________________________


3. Graph the two functions on the same coordinate grid an label.

________________________________________________________

4. What effect does the $0.75 per stem cost have on the graph of the Roses-R-Red function?

_________________________________________________________________________________

_________________________________________________________________________________

5. What effect does the $20.00 have on the graph? _______________________________________

_________________________________________________________________________________


6. What effect does the $0.50 per stem cost have on the graph of the Flower Power function?

_________________________________________________________________________________

_________________________________________________________________________________

7. What effect does the $60.00 have on the graph? _______________________________________

_________________________________________________________________________________

8. What is the significance of the point of intersection? ____________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

9. What is the point of intersection of the two graphs? _____________________________________

Show the work that supports your answer.

10. Which flower dealer offers the better deal and when? ___________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________


Activity 11: New Rose Offers

To entice potential new customers, Roses-R-Red decides to eliminate the $20.00 fixed charge.

According to its new offer, the drill team pays only for the roses they buy. When the Flower Power

learned about the new offer by its competitor, it immediately entered the price war by reducing its

$60.00 fixed charge to a $40.00 fixed charge.

1. How do the new offers compare to the original offers?___________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

2. Make a prediction. Will it change which company has the better offer?______________________

Support your prediction: ___________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________


3. From the description of each of the two new deals, complete the table and write new algebraic

rules that will determine the cost of n roses.

New Rose Offers

a.

Number of Roses

Process

Column

(Roses-R-Red)

Cost at

Roses-R-Red

Process

Column

(Flower Power)

Cost at

Flower Power

10 10(0.75) $7.50 40 + 10(0.50) $45.00

20

40

60

120

150

210

240

300

n

b. What patterns do you observe in the new table of values? _____________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

c. Compare the costs in this table to the costs in the first table. What changes do you observe?

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________


d. How many roses can you buy from Roses-R-Red for $65.00? __________________________


e. How many roses can you buy from Flower Power for $65.00? _________________________


f. Write an equation that represents the point where the two flower shops charge the same

amount.

________________________________________________________________________

g. At what point will the two flower dealers charge the same amount? ___________

What is the charge? __________________

h. Which company offers the better deal? ____________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________


Activity 12: Using Graphs for New Rose Offers

1. Graph both the original offer, y = 0.75x + 20, and the new offer, y = 0.75x, together.

a. What effect does subtracting $20.00 from the old rule have on the new graph of the Roses-

R-Red function? _____________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

2. Turn off the above two graphs. Graph both the original offer, y = 0.5x + 60, and the new offer,

y = 0.5x + 40, together.

a. What effect does subtracting $20.00 from the old rule have on the new graph of the Flower

Power function? _____________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

___________________________________________________________________________

3. What are the coordinates of the point where the original two functions intersect? _____________

4. What are the coordinates of the point where two new functions intersect? ___________________

5. What is the significance of this point of intersection? ____________________________________

_________________________________________________________________________________

_________________________________________________________________________________

6. What affect did the new pricing structure have on the point of intersection? Why? ____________

_________________________________________________________________________________

_________________________________________________________________________________


7. Which flower dealer now offers the better deal? ________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

8. Sketch the graphs of all four functions, label the graphs and label the relevant points of

intersection. Check your graphs on your graphing calculator. You may have to adjust your window

settings to see all your graphs.

______________________________________________________


Activity 13: The Birthday Gift

1. Susan‟s grandmother gave her $25.00 for her birthday. Instead of spending the money, she

decided to start a savings program by depositing the $25.00 in a non-interest paying savings club

account in the bank. Each week, Susan plans to deposit an additional $2.50 into the account. Make a

table of values for the situation.

Time (Weeks) Process Amount Saved (A)

$25.00

2. Write a function rule for the amount of money Susan will have after t weeks and define the

variables.

_________________________________________________________________________________

3. Find a viewing window for the problem situation and sketch your graph.

4. Justify your window choices.

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________


5. Graph the function rule by hand on the coordinate grid.

_____________________________________________

5. How much money will Susan have after 7 weeks? ____________________________________


6. Susan wants to buy a school ring. When will she have enough money to buy the $159.99 ring?

_________________________________________________________________________________



7. How would the line for the graph change if Susan deposits only $15.00 of the $25.00 given to her

by her grandmother? ________________________________________________________________

_________________________________________________________________________________

8. How would the line for the graph change if Susan deposits the $25.00 from her grandmother plus

another $15.00 she already had? _______________________________________________________

_________________________________________________________________________________

9. How would the line change if Susan deposits the $25.00 from her grandmother, but decides she

can only save $2.00 per week? ________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

10. What changes in the situation resulted in a change in the steepness of the line? ______________

_________________________________________________________________________________

11. What changes in the situation resulted in a change in the starting point of the line? __________

_________________________________________________________________________________

_________________________________________________________________________________

12. Write the coordinates of the point where the original line intersects the y-axis. _______________

This point is called the y-intercept. What do these coordinates represent in the context of this

situation? _________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________


Activity 14: Spending Money

1. Anton worked all summer and saved $1,090.00 and plans to spend the money during the school

year. He has budgeted spending $30.00 per week. Make a table of values for the situation.

Time (Weeks) Process Amount Saved (A)

$1,090.00

2. Write a function rule for the amount of money Anton will have after t weeks. Define the

variables.

_________________________________________________________________________________

3. Find a viewing window for the problem situation and sketch a graph.


_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________


5. Graph the function rule by hand on the coordinate grid.

_____________________________________________

5. How much money will Anton have after 11 weeks? ____________________________________


6. When will Anton run out of money?

_________________________________________________________________________________



7. How would the line for the graph change if Anton had initially saved $1,300 during the summer?

_________________________________________________________________________________

_________________________________________________________________________________

8. How would the line for the graph change if Anton spends $200.00 on school clothes and started

the school year with $890.00? ___________________________________________________

_________________________________________________________________________________

9. How would the line change if Anton starts with $1,090.00, but decides he will only spend $25.00

per week? ________________________________________________________________________

_________________________________________________________________________________

10. What change in the situation resulted in a change in the steepness of the line? ______________

_________________________________________________________________________________

11. What change in the situation resulted in a change in the starting point of the line? __________

_________________________________________________________________________________

12. Graph the three new situations (problems 7, 8, and 9) on the coordinate grid.

_____________________________________________


Activity 15: Money, Money, Money

1. Bill has $1,090.00 and he will spend $30.00 per week. Susan has $25.00 and will save $2.50 per

week. Determine a viewing window that includes both situations and sketch both graphs.


_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

3. Graph both function rules by hand on the coordinate grid.

________________________________________________________


4. When will Bill and Susan have the same amount of money in their accounts? _________________


a. Write an equation that would allow you to determine the answer.

___________________________________________________________________________

Define the variable:

6. How much money will Susan have when Bill is out of money? _________________________



Activity 16: At The Crossroads

FitnessPLUS Bodyworks

Initiation Fee $50 Initiation Fee $225

Monthly Fee $60 Monthly Fee $35

1. Candra wants to join a health club. Write two equations to compare the costs of belonging to each

health club (in slope-intercept form). Let C represent the total cost of membership. Let N represent

the number of months of membership.

Total Cost = Monthly fee times N + Initiation fee

FitnessPLUS ________________________________________________________

Bodyworks ________________________________________________________

2. Calculate the costs for 5 and 10 month membership for each of these two health clubs.

Cost of membership


5 Months

10 Months

3. Which health club membership will cost less if Candra joins for:

5 months? ______________________ For 10 months? ________________________

4. Without graphing, identify the slope and the vertical intercept of the graph of each cost equation.

Explain the meaning of each number in terms of the total cost of belonging to each health club.

FitnessPLUS: ____________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________


Bodyworks: _____________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________

5. Find the cost of a 7-month and 8-month membership for each health club.


7-month membership: __________________ ____________________

8-month membership: __________________ ____________________

What do you notice? ______________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________

________________________________________________________________________________


6. Graph each equation on the same graph. Label the axes, title the graph and use appropriate scales.

__________________________________________________________

7. Explain what the point where the two lines intersect means in the context of this scenario.

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________


8. Which health club costs less to belong to for one year? Use information from the graph to support

your answer.

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

9. Candra plans on belonging to a health club for many years. Make a recommendation to Candra

regarding which club to join from a purely financial perspective, but also communicate to her other

criteria she should use before making her decision.

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________


10. Of the people in attendance at a recent baseball game,

one-third had grandstand tickets,

one-fourth had bleacher tickets, and

the remaining 11,250 people in attendance had other tickets.

Which was the total number of people in attendance at the game?

A. 27,000

B. 20,000

C. 16,000

D. 18,000

11. Many sociologists predicted in 1990 that the trend shown on this graph will continue for many

years.

Which is the median age a man would marry for the first time in the year 2000?

A. Younger than 26.0

B. Between 26.0 and 26.9

C. Between 27.0 and 28.0

D. Older than 28.0


12. A painter uses 2 gallons of paint to cover a 400 square-foot area.

Which line on the graph best represents the total number of gallons of paint he will need to paint x

square feet?

A. l

B. m

C. n

D. q

13. The annual salary for a teacher is $34,000, plus an additional $500 per year for each year of

experience.

Which equation represents y, the annual salary for a teacher with x years of experience?

A. 500

34,000yx

B. 500

34,000yx

C. 500 34,000y x

D. 500 34,000y x


14. The table shows data collected from a timed practice period for a bicyclist riding at a constant

rate.

Which equation represents the linear relationship between y, the total number of minutes ridden, and

x, the total number of miles ridden?

A. 485

102

y x

B. 1 97

10 10y x

C. 1

2510

y x

D. 10

3y x

15. Which situation could be represented by the equation y = 3x + 5?

A. A bricklayer lays 5 bricks in 3 minutes. What is the total number of bricks he can

lay in x minutes?

B. An express package costs $5.00 plus $3.00 per pound to ship. What is the total cost of

shipping x pounds?

C. A jogger is 3 miles from home, jogging toward home at 5 miles per hour. What is the

total number of minutes it will take her to get home?

D. A math teacher gave some problems worth 5 points and a bonus problem worth 3 points.

What was the total value of the problems?

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DEPENDENT AND INDEPENDENT - North Thurston … and Independent 3 Activity 1: Function I. Read each numbered statement. Determine the two variables (in words) in each situation and