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Name _________________________________________________________________________________
MODULE 13
Relationships Using Two Variables Standard 6.EE.9:
● Use variables to represent two quantities in a real-world problem that change in relationship to one another.
● Write an equation to express the dependent variable in terms of the independent variable.
● Analyze the relationship between the dependent and independent variables using graphs and
tables, and relate these to the equation.
In Module 13, you will learn how to…
● ___ 13-1 Identify independent and dependent variables from tables and graphs. (6.EE.9)
● ___ 13-2 Write equations from tables. (6.EE.9)
● ___ 13-3 Represent algebraic relationships in tables and graphs. (6.EE.9)
● ___ 13-4 Model algebraic relationships in a table, graph, equation, and written description (6.EE.9)
Your Grade for 6.EE.9
The skills and concepts that you learn in this packet will appear as your grade for
6.EE.C.9 - Expressions & Equations
A = 4 EXCEEDS You exceed the learning targets in understanding or application.
B = 3 MEETS You have met all the learning targets for this standard.
C = 2 DEVELOPING You are approaching the standards or have only partial understanding.
D = 1 WELL BELOW You have not yet met many of the standards.
Name __________________________________________________________________________________ 6.EE.9 Lesson 13-1
Independent and Dependent Variables in Tables and Graphs Learning Target: I can identify independent and dependent variables in tables and graphs. (6.EE.9) Do Now
Directions: For each table, write an equation to represent the relationship between and x .y
x 1 2 3 4
y 7 14 21 28
_______________y =
x 1 2 3 4
y 7 8 9 10
_______________y =
Key Vocabulary
Many real-world situations involve two variable quantities in which one quantity depends on the other.
Independent Variable: The quantity that the other quantity (dependent variable) depends on, x
Dependent Variable: The quantity that depends on the other quantity (independent variable), y
The growth of a plant depends on the amount of water it receives.
Independent Variable: Amount of water plant receives
Dependent Variable: The growth of the plant
The number of pounds a person loses depends on the amount of exercise a person does.
Independent Variable: Amount of exercise a person does
Dependent Variable: Number of pounds a person loses
Directions: Underline the independent variable and box the dependent variable.
1) = number of miles bikedm = number of calories burnedc
2) = number of hotel rooms reservedh = number of family members on vacationf
3) = team’s scores = number of goals a soccer team makesg
4) = weight of yogurt at Menchie’sw = total costc
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Example 1- Identifying Independent and Dependent Variables from a Table
A freight train moves at a constant speed. The distance in miles that the train has traveled aftery hours is shown in the table.x
A) What are the two quantities in this situation? ______________________________________________________________________________________ B) Which of these quantities depends on the other? ______________________________________________________________________________________ C) What is the independent variable? ______________________________________________________________________________________ D) What is the dependent variable? ______________________________________________________________________________________ E) How far does the train travel each hour? ______________________________________________________________________________________ F) The relationship between the distance traveled by the train and the time in hours can be represented by an equation in two variables.
__________ __________ __________= •
G) Describe how the value of the independent variable is related to the value of the dependent variable. Is the relationship additive or multiplicative? ______________________________________________________________________________________ H) What are the units of the independent variable and of the dependent variable? ______________________________________________________________________________________ I) A rate is used in the equation. What is the rate? ______________________________________________________________________________________
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Exercise 1- Identifying Independent and Dependent Variables from a Table
1) Marcus reads for 30 minutes each night. He wants to determine the total number of minutes he will read over the course of a month.
A) Complete the table to show how many minutes Marcus has read in the first seven days.
C) Write an equation to show the relationship between the number of days that Marcus reads andd the total amount of time Marcus spent reading. t
Equation: ______________________________________
D) Describe how the value of the independent variable is related to the value of the dependent variable.
______________________________________________________________________________________
2) Kira designs websites. She can create three different websites each week.
A) Complete the table to show the number of websites Kira can design over the first 5 weeks.
C) Write an equation to represent the number of websites Kira can design when given any number d of weeks.w
Equation: ______________________________________
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Example 2- Identifying Independent and Dependent Variables from a Graph
In a graph, the independent variable is usually shown on the horizontal axis or x-axis and the dependent variable on the vertical axis or y-axis. An art teacher has 20 pounds of clay but wants to buy more clay for her class. The amount of clay x purchased by the teacher and the amount of clay available for the class are shown on the graph.y A) What are the two quantities in this situation? __________________________________________________ B) Which of these quantities depends on the other? __________________________________________________ C) What is the independent variable? __________________________________________________ D) What is the dependent variable? __________________________________________________ E) The relationship between the amount of clay purchased by the teacher the the amount of clay available to the class can be represented by an equation in two variables.
__________ __________ __________= + F) Describe how the value of the independent variable is related to the value of the dependent variable. Is this relationship additive or multiplicative? ______________________________________________________________________________________ ______________________________________________________________________________________ G) What are the units of the independent variable and of the dependent variable?
______________________________________________________________________________________
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Exercise 2- Identifying Independent and Dependent Variables from a Graph
1) Xin is buying beverages for a party that comes in packs of 8. Let be the number of packagesp Xin buys and be the total number of beverages.t B) Write an equation to show the relationship between the number of packages that Xin buys andp the total number of beverages that she has.t
Equation: ______________________________________ C) Describe the relationship between the independent and dependent variables. Is this relationship between the two variables additive or multiplicative? ______________________________________________________________________________________
______________________________________________________________________________________
Example 3- Describing Relationships Between Independent and Dependent Variables
A) The table shows a relationship between two variables, and .x y
Independent variable, x 0 1 2 3
Dependent variable, y 10 11 12 13
Describe a possible situation the table could represent.
__________________________________________
__________________________________________
The independent variable, is _________________,x
__________________________________________
The dependent variable, is __________________,y
__________________________________________
B) The graph shows a relationship between two variables. Describe a possible situation the graph could represent.
__________________________________________
__________________________________________
The independent variable, is ________________,x
__________________________________________
The dependent variable, is __________________,y
__________________________________________
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Problem Set
1) Teresa is buying glitter markers to put in gift bags. The table below shows the relationship between the number of gift bags, , and the number of glitter markers, , she needs to buy.x y
B) Write an equation to show the relationship between the number of gift bags and the number of glitterx y markers Teresa needs to buy.
Equation: ______________________________________ C) Describe the relationship between the independent and dependent variables. Is this relationship between the two variables additive or multiplicative.
______________________________________________________________________________________
______________________________________________________________________________________
2) The graph below shows the relationship between the number of tickets Lisa is ordering for a rafflet and the cost.c B) Write an equation to show the relationship between the number of tickets that Lisa orders andt the total cost. c
Equation: ______________________________________
C) Describe the relationship between the independent and dependent variables. Is this relationship between the two variables additive or multiplicative. ______________________________________________________________________________________
______________________________________________________________________________________
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3) Enoch can type 40 words per minute. The graph below shows the number of words typed andw the number of minutes spent typing. m
B) Independent variable: __________________________________ Dependent variable: ____________________________________
C) Equation: ____________________________________________ 4) A car travels at a constant rate of 60 miles per hour. A) Complete the table.
B) What is the independent variable, what is the dependent variable?
________________________________________________________________________________________ C) Write an equation to show the relationship between time and distance. x y
________________________________________________________________________________________ 5) A discount store has a special: 8 cans of juice for a dollar. A shopper decides that since the number of cans purchased is 8 times the number of dollars spent, the cost is the independent variable and the number of cans is the dependent variable. Do you agree? Explain.
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
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Name: ____________________________________ Date: __________________________ Period: _______
Homework for Lesson 13-1
Directions: Underline the independent variable and box the dependent variable.
1) = number of meters an object fallsd = number of secondst
2) = number of minutes a garden hose runsm = number of gallons of waterg
3) = number of rings on a tree trunkr = number of years growingy
4) = number of links in a chainn = length of the chainl
2) Gina’s cellular company charges $0.15 for each text message that she sends.
A)
B) Let be the amount of Gina’s bill b and be the number of texts sent.s
Write an equation that expresses the situation:
___________________________________
C) Complete the table:
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3) Robert is purchasing tickets for him and his friends to the school musical which cost $3 each.
A) Independent variable: _______________________ Dependent variable: ________________________
C) Complete the graph by labeling the andx − axes.y −
B) Let be the total cost that Robert spends c and be the number of tickets he buys.t
Write an equation that expresses the situation:
___________________________________
Spiral Review
1) A baseball pitcher won 60% of the games he pitched. If he pitched 35 baseball games, how many games did he win? How many games did he lose?
2) Ronnie drew a scale drawing of a house and its lot. In real life, the back patio is 12 meters wide. It is 2 millimeters wide in the drawing. What scale did Ronnie use? Use a proportion to solve.
1 millimeter = _______ meters
3) Tristan buys strawberry gum in packs of 15 pieces and blueberry gum in packs of 20 pieces. If Tristan wants to buy the same amount of each type of gum, what is the smallest number of pieces of each flavor that he must buy? Type of problem: GCF or LCM Solve:
4) Put these numbers in order from least to greatest:
________________________________________
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Name _________________________________________________________________________________ 6.EE.9 Lesson 13-2
Writing Equations from Tables
Learning Target: I can use an equation to show a relationship between two variables. (6.EE.9)
Do Now
Cara, a florist, is assembling bouquets of roses. She puts 15 roses in each bouquet. The table below shows the relationship between the number of bouquets Cara makes and the number of b r roses she uses. A) Complete the table.
C) Write an equation to represent the number of rosesr Cara uses the and number of bouquets Cara makes. Equation: ___________________________ b
Example 1- Writing an Equation Based on a Table
The relationship between two variables where one variable depends on the other can be represented in a table or by an equation.
An equation expresses the dependent variable in terms of the independent variable.
The table shows how much Amanda earns for walking 1, 2, or 3 dogs. Use the table to determine how much Amanda earns per dog. Then write an equation that models the relationship between the number of dogs walked and her earnings. Use your equation to complete the table.
Dogs walked, d 1 2 3 5 10 20
Earnings, e $8 $16 $24
What is the independent variable, what is the dependent variable?
_____________________________________________________________________________ A) According to the table, Amanda earns $_____ for each dog she walks. B) Amanda’s earnings depend on _____________________________________________________. C) Write an equation that relates the number of dogs Amanda walks to the amount she earns. Let represent earnings and represent dogs.e d
Equation: _________________________________
continued on the next page….
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D) Use your equation to complete the table for 5, 10, and 20 dogs walked.
E) If Amanda changed the amount earned per dog to $11, what equation could you write to model the relationship between number of dogs walked and earnings?
Equation: _________________________________
Example 1 Continued
When there is no real-world situation to consider, we usually say is the independent variable andx is the dependent variable.y
The value of depends on the value of .y x
Write an equation that expresses in terms of .y x
x 2 4 6 8 10
y 5 7 9 11 13
What is the independent variable, what is the dependent variable?
_________________________________________________________________________________ Step 1: Compare the and values to find a pattern.x y
________________________________________________________________________
Step 2: Use the pattern to write an equation expressing in terms of y .x
Equation: _________________________________
Exercise 1- Writing an Equation Based on a Table
1) When Ryan is 10, his brother Kyle is 15. When Ryan is 16, Kyle will be 21. When Ryan is 21, r k Kyle will be 26. A) Complete the table.
Ryan’s Age, r
Kyle’s Age, k
B) Write an equation that expresses Kyle’s age in terms of Ryan’s age.
Equation: _________________________________
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For each table, write an algebraic equation that expresses in terms of y .x
2)
x 12 11 10
y 10 9 8
Equation: ________________________
3)
x 10 12 14
y 25 30 35
Equation: ________________________
Example 2- Using Tables and Equations to Solve Problems
You can use tables and equations to solve real-world problems.
Meredith is playing video game. She earns the same number of points for each alien she captures. She earned 750 points for capturing 5 aliens and 1,350 points for capturing 9 aliens. Complete the table to help you determine the relationship between the aliens captured a and the total points. Then write an equation to represent the relationship. p
Aliens captured, a
Total points, p
Equation: _________________________________
Solve the equation to find how many points Meredith will earn if she captures 27 aliens.
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Exercise 2- Using Table and Equations to Solve Problems
1) Jameson downloaded one digital song for $1.35, two digital songs for $2.70, and 5 digital songs for $6.75. Complete the table to help you determine the relationship between the number of songs and the cost. .s c Then write an equation to represent the relationship.
Songs downloaded, s 1 2 5 10
Total cost, ($)c 1.35
Equation: _________________________________
Solve the equation to find the total cost if Jameson downloaded 25 songs.
Problem Set For each table, write an algebraic equation that expresses in terms of y .x
1)
x 5 4 3 2
y 10 9 8 7
Equation: ________________________
2)
x 1 2 3 4
y 3 6 9 12
Equation: ________________________
3)
x y
23 22
24 23
25 24
26 25
Equation: ________________________
Solve the equation to find the value of if is 55.,y x
4)
x y
56 8
49 7
42 6
35 5
Equation: ________________________
Solve the equation to find the value of if is 98.,y x
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5) Jamie enjoys doing puzzles in her free time. At the store, she bought 2 puzzles for $5.00 and 3 puzzles for $7.50. Complete the table to help you determine the relationship between the number of puzzles and the cost.p c Then write an equation to represent the relationship.
Puzzles bought, p 2 3 4 5
Total cost, ($)c 5.00 7.50
Equation: _________________________________
Solve the equation to find the total cost if Jamie bought 15 puzzles.
6) Marvin earns $8.25 per hour at his summer job. He wants to buy a video game system that costs $206.25.
A) Write an equation to model the relationship between the number of hours worked and amount earned h .e
_____________________________________________________ B) Solve your equation to find the number of hours Marvin needs to work in order to afford the video game system.
7) Compare the values in the table to the corresponding values. What pattern do you see?y − x − Use this pattern to write an equation that represents the relationship between the and values.x − y −
_______________________________________________ _______________________________________________ _______________________________________________
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8) Anna had this table as part of her homework last night. She had to use it to relate the independent variable to the dependent variable First, Anna used words to describe thex .y relationship and then she wrote an equation. She incorrectly said that the value of is 2 times they value of and that the equation is .x y = x2
x 1 4 5 6
y 2 5 6 7 A) Describe the relationship in words correctly. ______________________________________________________________________________________ B) Write an equation that represents the relationship between and x .y ________________________________________________________ C) Explain Anna’s likely error.
a) She used the correct number but the incorrect operation.
b) She used the correct operation but the incorrect number.
c) She considered only the first pair, not all four pairs.x, y)(
d) She formed the correct equation, but did not give the correct description in words.
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Name: ____________________________________ Date: __________________________ Period: _______
Homework for Lesson 13-2
For each table, write an algebraic equation that expresses in terms of y .x
1)
x 18 15 12 9
y 6 5 4 3
Equation: ________________________
Solve the equation to find the value of if is 45.,y x
2)
x 0 2 4 6
y 8 10 12 14
Equation: ________________________
Solve the equation to find the value of if is 273.,y x
3) A balloon rises to 100 feet in 4 minutes and 125 feet in 5 minutes. Complete the table to help you determine the relationship between the distance a balloon rises and thed m minutes it takes to rise. Then write an equation to represent the relationship.
Number of minutes, m 4 5 6 7
Distance, (feet)d
Equation: _________________________________
Solve the equation to find the distance the balloon rises in 12 minutes.
4) A student modeled the relationship in the table with the equation 4 . Explain the student’sx = y error. Then write an equation that correctly models the relationship.
x 2 4 6 8
y 8 16 24 32
Explain the error: ________________________________________________________________________
Equation: _____________________________________
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5) A taxicab service charges a flat fee of $8 plus an additional $2 per mile. Show the relationship between the total cost and the number of miles driven. t m
B) Write an equation to represent the situation: _____________________________________ C) Solve the equation to find the total cost for 10 miles.
Spiral Review
1) A dirt bike travels at 25 miles per hour. How far did it go in 3 hours?
2) Kylie earned a grade of 80% on her spelling test that had 20 problems. How many problems did Kylie answer correctly on her spelling test?
3) At $0.45 per dozen, how many dozen of oranges can you buy for $1.35?
4) Find the value of the expression: ( 4 + 6) 7 = ________44
÷ ÷
5) A preschool buys paint in bulk, then divides the paint into smaller portions for use in the classrooms. Today, they bought of a gallon of orange paint and divided it equally among 9 classrooms. How much9
10 orange paint did each classroom get?
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Name _________________________________________________________________________________ 6.EE.9 Lesson 13-3
Representing Algebraic Relationships in Tables and Graphs
Learning Target: I can use tables and graphs to represent algebraic relationships. (6.EE.9)
Do Now
An airplane travels at a constant rate of 800 miles per hour.
Complete the table to help you determine the relationship between the time and thet distance. Then write an equation to represent the relationship.d
Equation: _______________ Solve the equation to find the distance the airplane travels in 9 hours.
Opening- Representing Algebraic Relationships
Angie’s walking speed is 5 kilometers per hour, and May’s is 4 kilometers per hour. Show how the distance each girl walks is related to time. A) For each girl, complete the table comparing time and distance.
For every hour Angie walks, she travels ____ km. For every hour May walks, she travels ____ km. B) For each girl, make a graph showing her distance y as it depends on time x. Plot points from the table and connect them with a line. Write an equation for each girl that relates distance y to time x.
Angie’s Equation: ________________ May’s Equation: ________________ What is the independent variable, what is the dependent variable? Describe how you know. _________________________________________________________________________________
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Reflect on the Opening Activity: 1) How can you use the tables to determine which girl is walking faster? How can you use the graphs?
______________________________________________________________________________________
______________________________________________________________________________________
Example 1- Writing an Equation from a Graph
Cherise pays the entrance fee to visit the museum, then buys souvenirs at the gift shop. The graph shows the relationship between the total amount she spends at the museum and the amount she spends at the gift shop. A) Read the ordered pairs from the graph. Use them to complete a table comparing total spent to amount spent at the gift shop .y x
B) What is the pattern in the table?
________________________________________________________
C) Write an equation that expresses the total amount spent, , iny terms of the amount spent at the gift shop, .x
________________________________________________________ D) Draw a line through the points on the graph. Find the point that represents Cherise spending $18 at the gift shop. Use this point to find the total she would spend if she spent $18 at the gift shop. Then use your equation from Part C to verify your answer.
What is the independent variable? What is the dependent variable? Describe how you know.
______________________________________________________________________________________
_____________________________________________________________________________________
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Exercise 1- Writing an Equation from a Graph
1) Frank mows lawns in the summer to earn extra money. He can mow 3 lawns every hour he works. Make a table to show the relationship between the number of hours Frank works, and the number of,x lawns he mows, Graph the relationship and write an equation. Label the axes of your graph..y
Example 2- Graphing an Equation
An ordered pair that makes an equation like true is called a solution of the equation.x, y) ( x 1 y = + The graph of an equation represents all the ordered pairs that are solutions.
Graph the equation: x 1y = + Step 1: Make a table of values. Choose some values for and use the equation to find corresponding values for x . y
Step 2: Plot the ordered pairs from the table.
Step 3: Draw a line through the plotted points to represent all of the ordered pair solutions of the equation.
What is the independent variable? What is the dependent variable? _________________________________________________________________________________
Is the ordered pair (3.5, 4.5) a solution of the equation ? Explain. x 1y = +
______________________________________________________________________________________
______________________________________________________________________________________
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Exercise 2- Graphing an Equation
1) Graph the equation: . 2xy =
x x y2 = x, y)(
1
2
3
4
5
Problem Set
1) Students at Mills Middle School are required to work a certain number of community service hours. The table shows the number of additional hours several students worked beyond their required hours, as well as the total numbers of hours worked. A) Read the ordered pairs form the graph to make a table.
Additional hours, x
Total hours, y B) Write an equation that expresses the total hours in terms of the additional hours.
__________________________________________________ C) How many community service hours are students required to work? Explain.
______________________________________________________________________________________
2) Complete the table, plot the ordered pairs from the table in the graph, and write an equation.
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3) Graph the equation: . x 2.5y = +
x 2.5 yx + = x, y)(
0
1
2
3
4) Beth is using a map. Let represent a distance in centimeters on the map. To find an actualx distance in kilometers, Beth uses the equation y 8x.y = A) Make a table comparing a distance on the map to the actual distance.
Map distance (cm)
Actual distance (km)
B) Make a graph that compares the map distance to the actual distance. Label the axes of the graph. C) The actual distance between Town A and Town B is 64 kilometers. What is the distance on Beth’s map? Use the equation above to find the answer.
5) The cost of a personal pizza is $4. A drink costs $1. Anna wrote the equation to 4x 1y = + represent the relationship between total cost of buying meals that include one personal pizzay x and one drink. Describe Anna’s error and write the correct equation. ______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
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Name: ____________________________________ Date: __________________________ Period: _______
Homework for Lesson 13-3
1) The equation represents the total cost for movie tickets. Label the axes of the graph. 9xy = y x A) Make a table and a graph to represent the relationship between and x .y
Number of tickets, x
Total cost, ($)y B) Eight friends want to go see a movie. Would you prefer to use an equation, a table, or a graph to find the cost of 8 movie tickets? Explain how you would use your chosen method to find the cost.
2) Wilson Middle School’s 6th graders are trying to fundraise money for their Washington DC field trip. The student council decided to sell boxes of chocolate bars. Each bar sells for $1.50 and each box contains 20 bars. Below is a table of money collected for different numbers of boxes sold. A) Complete the table.
Boxes of Chocolate, b
Money collected, m
1 $30
2
3
4
5 $150
6
7
8
D) How much money will be collected if 100 boxes of candy are sold? Use your equation to solve.
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3) Graph the equation: . 1.5xy = A) Make a table to show the relationship.
B) Plot the points and draw a line through them.
4) Marcus plotted the points (0, 0), (6, 2), (18, 6) and (21, 7) on a graph. He wrote an equation for the relationship. Find another ordered pair that could be a solution of Marcus’s equation. Justify your answer. ______________________________________________________________________________________
______________________________________________________________________________________
Spiral Review
1) 40% of ________ is 60. 2) Tim ran the first half of a race 1.9 seconds faster than the second half. He ran the second half in 20.6 seconds. What was Tim’s total time for the race?
3) Evaluate the following numerical expressions:
Numerical Expression: Value:
2 1 + 3×
4 (3 + 3)·
2 + 1 1÷
5 2 5· ÷
3 (5 + 5) ×
Work Space:
4) On the coordinate plane, graph the points: (4, 5) and (4, -2). Then find the distance between the two points using absolute value.
Distance:
______________________________________
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Name _________________________________________________________________________________ 6.EE.9 Lesson 13-4
Modeling Algebraic Relationships in a Table, Graph, Equation, and Written Description
Learning Target: I can model algebraic relationships in a table, graph, equation, and written description (6.EE.9)
Do Now Graph the equation: y = x + 6.
x + 6 = x y ( , )x y
1
2
3
4
Opening
So far in this module, we have learned about equations, tables, and graphs and how they can each represent the information for a given situation. Well, if they can all give the same information, then why do we have three different ways to represent the same thing? Good question! Let’s take a look at the advantages for each method. Plotting a Relationship (Graphing): The most important use for graphing is that it can visually represent the relationship between our independent variable ( ) and our dependent variable ( ). Often, this relationship is expressed this way: ifx y you tell me , I can tell you . The graph that is drawn shows the visual representation of solutions to anx y equation. Equations: For any number, even really big numbers, instead of drawing a large graph, we can just use an equation to quickly find if we know what is. As an equation, this sort of relationship looks like this:y x
= some expression involving Another way of saying this is “We have in terms of .y x y x Examples: If you plug in a number for in either of these equations, youx d can calculate a value for .y
2x 1y = + x x 2y = 2 − 3 +
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Tables: A table is an organized list of solutions to its equation. For example, take . You can get a set of 2x 1y = +
’s by plugging in different values of . Start by making a table.y x
x 2x 1y = + y
0 2(0) 1y = + 1
1 2(1) 1y = + 3
2 2(2) 1y = + 5
Now that you have some values, see what you can do with them. You can say that when equals 0, x y equals 1. These two values form a pair. You can show this relationship by plotting the point (0,1) on a graph. Similarly, you can plot all the other points that represent an , pair from your table.x y Below is the graph of our table above.
26
Example 1
Jeremy is rollerblading in the park at a speed of 3 feet per second. How many feet will he travel after 9 seconds? Let be the total distance that Jeremy travels and be the number of seconds he rollerblades. d s
A) Write an equation that expresses the situation: __________________________________________ B) Complete the table:
Independent Variable: ________________ Dependent Variable: _________________
C) Graph your table of Jeremy’s distance for every second he skates.
27
Exercise 1
1) A grizzly bear eats fifteen fishes everyday. How many fishes does the bear eat after 6 days? Let be the total amount of fishes that the grizzly bear eats and be the number of days. t d
A) Write an equation that expresses the situation: __________________________________________ B) Complete the table:
Independent Variable: ________________ Dependent Variable: _________________
C) Graph your table of total amount the bear eats.
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Exercise 2
Equation: x 8y = 4 +
Graph:
A) From the equation and graph above, write a scenario that matches the information given: ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ B) Complete the table:
Independent Variable: ________________ Dependent Variable: _________________
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Name _________________________________________________________________________________ Module 13 Review
Module 13 Study Guide Review Lesson Practice
Lesson 13-1: Independent and Dependent Variables in Tables and Graphs
1) Underline the independent variable and box the dependent variable.
= total amount spentt
= number of shirts boughts
2) Underline the independent variable and box the dependent variable.
= number of eggs in the cartone
= total cost of the eggst
3) Ms. Samuel is purchasing pencils for the students in her classroom. The pencils are sold in boxes. Each box has 12 pencils. A) Complete the table to show the relationship between the number of boxes and the number of pencils.b p B) Determine which variable is independent and which is dependent. Independent variable: ________________________ Dependent variable: _________________________ C) Write an equation to show the relationship between the number of boxes and the number of pencils Ms.b p Samuel purchased.
Equation: ____________________________
4) The Clark family is on a road trip. The graph below shows the relationship between the number of miles the family drives and the number of hours they drive.m h A) Determine which variable is independent and which is dependent. Independent variable: ___________________ Dependent variable: ____________________ B) Write an equation to show the relationship between the number of miles and the numberm of hours the family drives.h Equation: ____________________________
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Lesson 13-2: Writing Equations from Tables
1)
x y
10 7
20 17
30 27
40 37
Equation: ________________________
Solve the equation to find the value of ,y if is 90. x
2) x y
1 5
2 10
3 15
4 20
Equation: ________________________
Solve the equation to find the value of ,y if is 36. x
3) Kyla spends 60 minutes of each day exercising. Let be the number of days that Kylad exercises, and let represent the total minutes of exercise in a given time frame. Show m the relationship between the number of days that Kyla exercises and the total minutes that she exercises.
B) Write an equation to represent the situation: ______________________________ C) Solve the equation to find the total number minutes Kyla exercises if she exercises for 14 days.
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4) Emma was given 5 seashells. Each week she collected 3 more seashells. Let bew the number of weeks Emma collects seashells and be the number of seashells she hass total. A) Complete the table to model the situation.
Number of weeks, w 0 1 2 3 4 5
Total number of seashells, s
C) Solve the equation to find the total number of seashells Emma collected in 9 weeks.
Lesson 13-3: Representing Algebraic Relationships in Tables and Graphs
1) Each week Quentin earns $30 for delivering newspapers and he saves this money. Create a graph that shows the total amount of money Quentin has saved from Week 1 through Week 8. Write an equation that represents the relationship between the number of weeks that Quentin saved his money, and the total amount of money in dollars he,w has saved, Then, name the independent and dependent variables..s
Equation: ___________________________
Independent variable: _________________ Dependent variable: __________________
32
2) Graph the equation: x 3y = +
3) Graph the equation: 10 xy = −
4) The graph shows the number of bracelets Olivia can make in an hour. A) Read the ordered pairs from the graph to make a table.
B) Write an equation to model the relationship: _____________________________________ C) How many hours will it take Olivia to make 32 bracelets? Solve using the equation.
33
