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## Go Math Grade 6 Answer Key Chapter 9 Independent and Dependent Variables

The Independent and Dependent Variables chapter consists of the topics like equations and tables, analyze relationships, graphs etc. It is essential for students to know the relationship between the graphs and tables in this chapter. You can know different methods of solving the problems by using Go Math Grade 6 Solution Key Chapter 9 Independent and Dependent Variables. All you have to do is to tap the below-given links.

**Lesson 1: Independent and Dependent Variables**

- Share and Show – Page No. 493
- Unlock the Problem – Page No. 494
- Independent and Dependent Variables – Page No. 495
- Lesson Check – Page No. 496

**Lesson 2: Equations and Tables**

- Share and Show – Page No. 499
- Cause and Effect – Page No. 500
- Equations and Tables – Page No. 501
- Lesson Check – Page No. 502

**Lesson 3: Problem Solving • Analyze Relationships**

- Share and Show – Page No. 505
- On Your Own – Page No. 506
- Problem Solving Analyze Relationships – Page No. 507
- Lesson Check – Page No. 508

**Mid-Chapter Checkpoint**

**Lesson 4: Graph Relationships**

- Share and Show – Page No. 513
- Problem Solving + Applications – Page No. 514
- Graph Relationships – Page No. 515
- Lesson Check – Page No. 516

**Lesson 5: Equations and Graphs**

- Share and Show – Page No. 519
- Problem Solving + Applications – Page No. 520
- Equations and Graphs – Page No. 521
- Lesson Check – Page No. 522

**Chapter 9 Review/Test**

- Chapter 9 Review/Test – Page No. 523
- Chapter 9 Review/Test – Page No. 524
- Chapter 9 Review/Test – Page No. 525
- Chapter 9 Review/Test – Page No. 526
- Chapter 9 Review/Test – Page No. 527
- Chapter 9 Review/Test – Page No. 528

### Share and Show – Page No. 493

**Identify the independent and dependent variables. Then write an equation to represent the relationship between them.**

Question 1.

An online store lets customers have their name printed on any item they buy. The total cost c in dollars is the price of the item p in dollars plus $3.99 for the name.

Type below:

________________

Answer: c = p + $3.99

Explanation:

The independent variable is c, the price of the item because it is not going to depend on anything else.

The dependent variable is p because the total cost depends on how many items there are, whether your name is marked on it, etc.

The equation would be:

c = p + $3.99

Question 2.

A raft travels downriver at a rate of 6 miles per hour. The total distance d in miles that the raft travels is equal to the rate times the number of hours h.

Type below:

________________

Answer: d = 6 × h

Explanation:

Speed of the raft= 6 miles per hour

Total distance (d) of the raft = rate × number of hours h

The dependent variable is the number of hours h

The independent variable is distance d.

The equation would be:

d = 6 × h

Question 3.

Apples are on sale for $1.99 a pound. Sheila buys p pounds of apples for a total cost of c dollars.

Type below:

________________

Answer: c = p × $1.99

Explanation:

Apples are on sale for $1.99 a pound

p = pounds of apples

c = total cost of dollars

The equation would be:

c = p × $1.99

c is the independent variable.

p is the dependent variable.

**On Your Own**

**Identify the independent and dependent variables. Then write an equation to represent the relationship between them.**

Question 5.

Billy has $25. His father is going to give him more money. The total amount t Billy will have is equal to the amount m his father gives him plus the $25 Billy already has.

Type below:

________________

Answer: t = m + $25

Explanation:

Billy has $25. His father is going to give him more money.

The total amount t Billy will have is equal to the amount m his father gives him plus the $25 Billy already has.

The equation would be:

t = m + $25

t is the independent variable

m is the dependent variable.

Question 6.

Connect Symbols and Words Describe a situation that can be represented by the equation c = 12b.

Type below:

________________

Answer:

Melinda is making necklaces. She uses 12 beads for each necklace. The total number of beads b depends on the cost of the necklace c.

The equation is c = 12n

Question 7.

Belinda pays $4.25 for each glass she buys. The total cost c is equal to the price per glass times the number of glasses n plus $9.95 for shipping and handling. Write an equation and use it to find how much it will cost Belinda to buy 12 glasses.

Type below:

________________

Answer:

Belinda pays $4.25 for each glass she buys. The total cost c is equal to the price per glass times the number of glasses n plus $9.95 for shipping and handling.

The equation is: c = 4.25n + 9.95

Now we have to find the cost of 12 glasses.

c = 4.25(12) + 9.95

c = 60.95

It takes $60.95 to buy 12 glasses.

### Unlock the Problem – Page No. 494

Question 8.

Benji decides to save $15 per week to buy a computer program. Write an equation that models the total amount t in dollars Benji will have saved in w weeks.

a. What does the variable t represent?

Type below:

________________

Answer: t represents the total amount in dollars Banji saved.

Question 8.

b. Which is the dependent variable? Which is the independent variable? How do you know?

Type below:

________________

Answer:

w is the dependent variable.

t is the independent variable.

w is dependent because it represents the number of weeks. So, we have to multiply 15 by w.

t is an independent variable because t determines the value of a dependent variable.

Question 8.

c. How can you find the total amount saved in w weeks?

Type below:

________________

Answer: We can find the total amount saved in w weeks by multiplying 15 with w.

Question 8.

d. Write an equation for the total amount that Benji will have saved.

Type below:

________________

Answer: t = 15w

Question 9.

Coach Diaz is buying hats for the baseball team. The total cost c is equal to the number of hats n that he buys times the sum of the price per hat h and a $2 charge per hat to have the team name printed on it. Write an equation that can be used to find the cost of the hats.

Type below:

________________

Answer: c = n + 2h

Explanation:

Coach Diaz is buying hats for the baseball team.

The total cost c is equal to the number of hats n that he buys times the sum of the price per hat h and a $2 charge per hat to have the team name printed on it.

c represents the total cost.

n is the number of hats

h is the price per hat.

The equation is c is equal to the number of hats plus price per hat and $2.

c = n + 2h

Question 10.

A steel cable that is \(\frac{1}{2}\) inch in diameter weighs 0.42 pound per foot. The total weight in pounds w is equal to 0.42 times of the number of feet f of steel cable. Choose the letter or equation that makes each sentence true.

The independent variable is ______________ .

The dependent variable is ______________ .

The equation that represents the relationship between the variables is ______________ .

Answer:

A steel cable that is \(\frac{1}{2}\) inch in diameter weighs 0.42 pound per foot.

The total weight in pounds w is equal to 0.42 times of the number of feet f of steel cable.

The equation would be:

w = 0.2f

f is the dependent variable

w is the dependent variable.

### Independent and Dependent Variables – Page No. 495

**Identify the independent and dependent variables. Then write an equation to represent the relationship between them.**

Question 2.

An online clothing store charges $6 for shipping, no matter the price of the items. The total cost c in dollars is the price of the items ordered p plus $6 for shipping.

Type below:

________________

Answer: c = p + 6

Explanation:

Given,

An online clothing store charges $6 for shipping, no matter the price of the items.

The total cost c in dollars is the price of the items ordered p plus $6 for shipping.

The equation would be:

c = p + $6

where c = cost in dollars

p is the price of items

The independent variable is c.

The dependent variable is p

Question 3.

Melinda is making necklaces. She uses 12 beads for each necklace. The total number of beads b depends on the number of necklaces n.

Type below:

________________

Answer: b = 12n

Explanation:

Melinda is making necklaces. She uses 12 beads for each necklace.

The total number of beads b depends on the number of necklaces n.

b = total number of beads

n = number of necklaces

The equation would be:

b = 12n

b is the independent variable

n is the dependent variable.

**Problem Solving**

Question 4.

Maria earns $45 for every lawn that she mows. Her earnings e in dollars depend on the number of lawns n that she mows. Write an equation that represents this situation.

Type below:

________________

Answer: e = 45n

Explanation:

Maria earns $45 for every lawn that she mows.

Her earnings e in dollars depend on the number of lawns n that she mows.

e = earnings in dollars

n = number of lawns

The equation would be:

e = 45n

e is the independent variable.

n is the dependent variable.

Question 6.

Write a situation in which one unknown is dependent on another unknown. Write an equation for your situation and identify the dependent and independent variables.

Type below:

________________

Answer:

Byron is playing a game. He earns 10 points for each question he answers correctly. His total score s equals the number of correct answers a time a.

Answer:

Dependent variable: s

Independent variable: a

Equation: s = 10a

### Lesson Check – Page No. 496

Question 1.

There are 12 boys in a math class. The total number of students s depends on the number of girls in the class g. Write an equation that represents this situation.

Type below:

________________

Answer: s = 12 + g

Explanation:

There are 12 boys in a math class.

The total number of students s depends on the number of girls in class g.

The equation would be:

s = 12 + g

s is the independent variable.

g is the dependent variable.

**Spiral Review**

Question 3.

The formula F = \(\frac{9}{5}\)C + 32 gives the Fahrenheit temperature for a Celsius temperature of C degrees. Gwen measured a Celsius temperature of 35 degrees. What is this temperature in degrees Fahrenheit?

______ °F

Answer: 95 degrees

Explanation:

The formula F = \(\frac{9}{5}\)C + 32 gives the Fahrenheit temperature for a Celsius temperature of C degrees.

C = 35

F = 9C ÷ 5 + 32

F = 9(35) ÷ 5 + 32

F = 315 ÷ 5 + 32

F = 63 + 32

F = 95 degrees

Question 4.

Write an equation to represent this sentence. The difference of a number n and 1.8 is 2.

Type below:

________________

Answer: n – 1.8 = 2

Explanation:

The difference of a number n and 1.8 is 2.

The phrase difference is nothing but subtraction.

The equation would be:

n – 1.8 = 2

Question 6.

Graph x ≤ ^{–}4.5 on a number line.

Type below:

________________

Answer:

### Share and Show – Page No. 499

**Use the equation to complete the table.**

Question 1.

y = x + 3

Type below:

________________

Answer:

Substitute the value of x in the above equation.

The equation is x + 3.

Question 2.

y = 2x + 1

Type below:

________________

Answer:

Substitute the value of x in the above equation.

The equation is y = 2x + 1

**On Your Own**

**Write an equation for the relationship shown in the table. Then find the unknown value in the table.**

Question 3.

Type below:

________________

Answer:

The equation is y = 2x

The output is multiple of 2 and x

For x = 10

The output is y = 2x

y = 2 × 10 = 20

Question 4.

Type below:

________________

Answer:

y = x ÷ 2

The output is the quotient of x and 2.

The output for x = 40 is

y = 40 ÷ 2

y = 20

Question 5.

The table shows the current cost of buying apps for a cell phone. Next month, the price of each app will double. Write an equation you can use to find the total cost y of buying x apps next month.

Type below:

________________

Answer: y = 3x

Explanation:

The equation is multiple of 3 and x.

The equation is y = 3x

Question 6.

A beach resort charges $1.50 per hour plus $4.50 to rent a bicycle. The equation c = 1.50x + 4.50 gives the total cost c of renting a bicycle for x hours. Use numbers and words to explain how to find the cost c of renting a bicycle for 6 hours.

Type below:

________________

Answer:

A beach resort charges $1.50 per hour plus $4.50 to rent a bicycle.

The equation c = 1.50x + 4.50 gives the total cost c of renting a bicycle for x hours.

For x = 1

c = 1.50(1) + 4.50

c = 1.50 + 4.50

c = $6.00

For x = 2

c = 1.50(2) + 4.50

c = 3.00 + 4.50

c = $7.50

For x = 3

c = 1.50(3) + 4.50

c = 4.50 + 4.50

c = $9.00

For x = 4

c = 1.50(4) + 4.50

c = 6.00 + 4.50

c = $10.50

### </aCause and Effect – Page No. 500

The reading skill cause and effect can help you understand how a change in one variable may cause a change in another variable.

In karate, a person’s skill level is often shown by the color of his or her belt. At Sara’s karate school, students must pass a test to move from one belt level to the next. Each test costs $23. Sara hopes to move up 3 belt levels this year. How will this affect her karate expenses?

Question 7.

Write an equation to show the relationship between cause and effect. Then use the equation to solve the problem.

Type below:

________________

Answer: y = 23x

Explanation:

Let x represent the number of belt levels Sara moves up and let y represent the increase in dollars in her karate expenses.

Write the equation:

y = 23x

Sara plans to move up 3 levels, so replace x with 3

y = 23 × 3

y = 69

So, if Sara moves up 3 belt levels this year, her karate expenses will increase by $69.

**Write an equation to show the relationship between cause and effect. Then use the equation to solve the problem.**

Question 8.

Classes at Tony’s karate school cost $29.50 per month. This year he plans to take 2 more months of classes than he did last year. How will this affect Tony’s karate expenses?

Type below:

________________

Answer:

The equation is y = 29.50x

where x is the number of additional classes

y is the increase in dollars in expenses.

Tony plans to take 2 more months of classes so his expenses will increase by y = 29.5 × 2 = $59

### Equations and Tables – Page No. 501

**Use the equation to complete the table.**

Question 1.

y = 6x

Type below:

________________

Answer:

The equation is y = 6x

Substitute the value of x in the above equation.

Question 2.

y = x − 7

Type below:

________________

Answer:

The equation is y = x – 7

Substitute the value of x in the equation.

Use the equation to get the output y.

Question 3.

y = 3x + 4

Type below:

________________

Answer:

The equation is y = 3x + 4

Substitute the value of x in the above equation.

Use the equation to get the output y.

**Write an equation for the relationship shown in the table. Then find the unknown value in the table.**

Question 4.

Type below:

________________

Answer: y = 8x

Explanation:

The equation is the multiple of 8.

The equation is y = 8x

Substitute x = 3 in the equation.

y = 8(3) = 24

Thus the unknown value is 24.

Question 5.

Type below:

________________

Answer: y = x ÷ 2

Explanation:

The equation is divisible by 2.

The equation is y = x ÷ 2

Substitute x = 22 in the equation.

y = x ÷ 2

y = 22 ÷ 2

y = 11

Therefore the unknown value is 11.

**Problem Solving**

Question 7.

Write an equation for the relationship shown in the table. Then use the equation to find the estimated number of shrimp in a 5-pound bag.

Type below:

________________

Answer: y = 24x

Explanation:

The equation is the multiple of 24.

The equation is y = 24x

Question 8.

Write a word problem that can be represented by a table and equation. Solve your problem and include the table and equation.

Type below:

________________

Answer:

Susie ran a race. She ran 5 miles an hour and the race took her x hours to complete.

y = 5x

Use the equation to get the output y.

### Lesson Check – Page No. 502

Question 1.

Write an equation that represents the relationship shown in the table.

Type below:

________________

Answer: y = x – 4

Explanation:

The relationship between x and y is y = x – 4.

We get the output when we subtract 4 from x.

Question 2.

There is a one-time fee of $27 to join a gym. The monthly cost of using the gym is $18. Write an equation for the relationship that gives the total cost y in dollars of joining the gym and using it for x months.

Type below:

________________

Answer: y = 18x + 27

Explanation:

Given,

There is a one-time fee of $27 to join a gym. The monthly cost of using the gym is $18.

Here y represents the total coast in dollars of joining the gym.

x represents months.

So, the equation would be: y = 18x + 27

**Spiral Review**

Question 3.

Mindy wants to buy several books that each cost $10. She has a coupon for $6 off her total cost. Write an expression to represent her total cost in dollars for b books.

Type below:

________________

Answer: 10b – 6

Explanation:

Given,

Mindy wants to buy several books that each cost $10.

She has a coupon for $6 off her total cost.

b represents the total cost in dollars for b books.

So, the equation to represent the total cost is 10b – 6.

Question 5.

Which of the following are solutions to the inequality n > ^{–}7?

n = ^{–}7 n = ^{–}6.9 n = ^{–}7.2 n = ^{–}6\(\frac{1}{2}\)

Type below:

________________

Answer: n = -7

Explanation:

Substitute the value of n in the inequality.

n > ^{–}7

n = -7

-7 > -7

Thus -7 is the solution.

n = ^{–}6.9

-6.9 > -7

-6.9 is not the solution.

n = ^{–}7.2

-7.2 > -7

-7.2 is less than – 7

Thus -7.2 is not the solution.

n = ^{–}6\(\frac{1}{2}\)

^{–}6\(\frac{1}{2}\) > -7

^{–}6\(\frac{1}{2}\) is not the solution.

Question 6.

Marcus sold brownies at a bake sale. He sold d dollars worth of brownies. He spent $5.50 on materials, so his total profit p in dollars can be found by subtracting $5.50 from his earnings. Write an equation that represents this situation.

Type below:

________________

Answer: p = d – 5.50

Explanation:

Marcus sold brownies at a bake sale. He sold d dollars worth of brownies.

He spent $5.50 on materials, so his total profit p in dollars can be found by subtracting $5.50 from his earnings.

p represents the total profit in dollars.

d is the dollars worth of brownies.

The equation is p = d – 5.50

### Share and Show – Page No. 505

Question 1.

A soccer coach is ordering shirts for the players. The table shows the total cost based on the number of shirts ordered. How much will it cost the coach to order 18 shirts?

$ _______

Answer: 270

Explanation:

First, find a pattern and write an equation.

The cost is $15 multiplied by the number of shirts.

c = $15 × n

Next, use the equation to find the cost of 18 shirts.

c = $15 × n

c = $15 × 18

c = $270

So, the cost of 18 shirts is $270.

Question 2.

What if the coach spent $375 to purchase a number of shirts? Could you use the same equation to find how many shirts the coach bought? Explain.

Type below:

________________

Answer:

Yes, I could use the same equation.

I could substitute 375 for the variable c and solve for n.

Question 3.

The table shows the number of miles the Carter family drove over time. If the pattern continues, will the Carter family have driven more than 400 miles in 8 hours? Explain.

Type below:

________________

Answer: 376 miles

Explanation:

First, find a pattern and write an equation.

The distance is 47 miles multiplied by the number of hours.

y = 47 × x

Next, use the equations to find the distance for 8 hours.

y = 47x

y = 47 × 8

y = 376

So, the family will have driven 376 miles in 8 hours, which is less than 400 miles.

### On Your Own – Page No. 506

Question 5.

A group of dancers practiced for 4 hours in March, 8 hours in April, 12 hours in May, and 16 hours in June. If the pattern continues, how many hours will they practice in November?

_______ hours

Answer: 36 hours

Explanation:

Given that, a group of dancers practiced for 4 hours in March, 8 hours in April, 12 hours in May, and 16 hours in June.

The equation would be h = 4m

m = 9

h = 4 × 9 = 36

Thus the group practiced 36 hours in the month of November.

Question 6.

The table shows the number of hours Jacob worked and the amount he earned each day.

At the end of the week, he used his earnings to buy a new pair of skis. He had $218 left over. How much did the skis cost?

$ _______

Answer: 142

Explanation:

First, add the total amount he earned.

60 + 84 + 72 + 96 + 48 = 360

Jacob earned $360 for the week.

If he has $218 leftover, this means that the cost of the skis is 360 – 218 = 14

Therefore the cost of the skis is $142.

Question 7.

Pose a Problem Look back at Problem 6. Use the data in the table to write a new problem in which you could use the strategy to find a pattern. Then solve the problem.

Type below:

________________

Answer:

How much money would Jacob earn if he worked for 10 hours?

From the table, we can see that the pattern is that Jacob earns $12 per hour.

The equation is s = 12h

Where s is the total pay and h is the number of hours worked.

s = 12h

s = 12 × 10

s = 120

Thus Jacob earned $120 for 10 hours.

Question 8.

Draw Conclusions Marlon rode his bicycle 9 miles the first week, 18 miles the second week, and 27 miles the third week. If the pattern continues, will Marlon ride exactly 100 miles in a week at some point? Explain how you determined your answer.

Type below:

________________

Answer: No, Marlon will not ride exactly 100 miles in a week at some point.

Each number in the pattern is a multiple of 9 and 100 is not a multiple of 9.

Question 9.

A diving instructor ordered snorkels. The table shows the cost based on the number of snorkels ordered.

If the diving instructor spent $1,024, how many snorkels did he order? Use numbers and words to explain your answer.

_______ snorkels

Answer: 32

Explanation:

Use the table to find the equation.

c represents the cost based on the number of snorkels.

s represents the number of snorkels

The equation would be:

c = 32s

The diving instructor spent $1,024

c = 1024

1024 = 32s

s = 1024/32

s = 32

Thus the diving instructor gets 32 snorkels for $1024.

### Problem Solving Analyze Relationships – Page No. 507

**The table shows the number of cups of yogurt needed to make different amounts of a fruit smoothie. Use the table for 1–3.**

Question 1.

Write an equation to represent the relationship.

Type below:

________________

Answer: c = 3b

Explanation:

c represents number of cups of yogurt

b represents the batches

From the table, we can observe that b is multiplied with 3 to get cups of yogurt.

So, the equation to find the number of cups of yogurt is c = 3b

Question 2.

How much yogurt is needed for 9 batches of smoothie?

_______ cups

Answer: 27

Explanation:

Given that there are 9 batches of smoothie.

By using the above equation we can find the number of cups.

c = 3b

c = 3 × 9 = 27 cups

Thus 27 cups of yogurt is need to make 9 batches of smoothie.

Question 3.

Jerry used 33 cups of yogurt to make smoothies. How many batches did he make?

_______ batches

Answer: 11 batches

Explanation:

Jerry used 33 cups of yogurt to make smoothies.

Use the equation to find the batches.

c = 3b

33 = 3b

b = 33/3

b = 11

Therefore jerry made 11 batches of smoothie.

**The table shows the relationship between Winn’s age and his sister’s age. Use the table for 4–5.**

Question 4.

Write an equation to represent the relationship.

Type below:

________________

Answer: s = w + 4

Explanation:

By using the table we can find the relationship between wine’s age and wine’s sister’s age.

Winn’s sister’s age will be the sum of Winn’s age and 4.

So, the equation is s = w + 4

Question 5.

When Winn is 14 years old, how old will his sister be?

_______ years old

Answer: 18

Explanation:

Use the equation s = w + 4

W = 14 years

s = 14 + 4

s = 18 years

Thus winn’s sister’s age is 18 years.

Question 6.

Write a problem for the table. Use a pattern and an equation to solve your problem.

Type below:

________________

Answer: m = 16h

Explanation:

Jerry runs 16 miles per hour. How many miles he can run in 5 hours?

The equation is m = 16h

m = 16 × 5 = 80 miles

Therefore jerry runs 80 miles in 5 hours.

### Lesson Check – Page No. 508

Question 1.

The table shows the total cost c in dollars of n gift baskets. What will be the cost of 9 gift baskets?

Answer: $108

Explanation:

By seeing the above we can say that the equation is

c = 12n

n = 9

Use the equation to find the cost of 9 gift baskets.

c = 12 × 9

c = $108

Thus the cost of 9 gift baskets is $108.

Question 2.

The table shows the number of minutes m that Tara has practiced after d days. If Tara has practiced for 70 minutes, how many days has she practiced?

_______ days

Answer: 2 days

Explanation:

The table shows the number of minutes m that Tara has practiced after d days.

The equation would be

m = 35d

If Tara has practiced for 70 minutes

m = 70

Use the equation to find the number of days she practiced.

70 = 35d

d = 70/35

d = 2 days

Thus Tara has practiced 2 days.

**Spiral Review**

Question 3.

Soccer shirts cost $15 each, and soccer shorts cost $18 each. The expression 15n + 18n represents the total cost in dollars of n uniforms. Simplify the expression by combining like terms.

Type below:

________________

Answer: 33n

Explanation:

Soccer shirts cost $15 each, and soccer shorts cost $18 each.

The expression 15n + 18n represents the total cost in dollars of n uniforms.

Now combine the like terms.

15n + 18n = 33n

Question 4.

What is an equation that represents the relationship in the table?

Type below:

________________

Answer: y = x ÷ 2

Explanation:

By seeing the above table we can find the relationship between x and y.

y is the quotient of x and 2.

We get the value of y when you divide x by 2.

The equation is y = x ÷ 2

Question 6.

Marisol plans to make 9 mini-sandwiches for every 2 people attending her party. Write a ratio that is equivalent to Marisol’s ratio.

Type below:

________________

Answer: 9:2

Explanation:

Given that, Marisol plans to make 9 mini-sandwiches for every 2 people attending her party.

The ratio will be 9:2

Now we need to write the equivalent ratio for the 9 sandwiches for every 2 people i.e, 9:2

We know that the equivalent ratio can be written as

9/2 × 3/3 = 27/6

9/2 × 5/5 = 45/6

Thus the equivalent fractions are 27/6 and 45/6.

### Mid-Chapter Checkpoint – Vocabulary – Page No. 509

**Choose the best term from the box to complete the sentence.**

Question 1.

A(n) _____ has a value that determines the value of another quantity.

Type below:

________________

Answer: Independent variable

An Independent variable has a value that determines the value of another quantity.

Question 2.

A variable whose value is determined by the value of another quantity is called a(n) _____.

Type below:

________________

Answer: Dependent variable

A variable whose value is determined by the value of another quantity is called a Dependent variable.

**Concepts and Skills**

**Identify the independent and dependent variables.**

**Write an equation for the relationship shown in the table. Then find the unknown value in the table.**

Question 5.

Type below:

________________

Answer: 49

Explanation:

The equation is y = 7x

x = 7

y = 7 × 7 = 49

Thus the unknown value y is 49.

Question 6.

Type below:

________________

Answer: 12

Explanation:

The equation for the above table is

y = x ÷ 5

Use the equation to find the value of y where x = 60

y = 60 ÷ 5

y = 12

Thus the unknown value is 12.

**Write an equation that describes the pattern shown in the table.**

Question 7.

The table shows how the number of pepperoni slices used depends on the number of pizzas made.

Type below:

_______________

Answer: y = 17x

Explanation:

The table shows how the number of pepperoni slices used depends on the number of pizzas made.

y is 17 times of x.

The equation for the above table is y = 17x

Question 8.

Brayden is training for a marathon. The table shows how the number of miles he runs depends on which week of training he is in.

Type below:

________________

Answer: m = w + 5

Explanation:

Brayden is training for a marathon. The table shows how the number of miles he runs depends on which week of training he is in.

m is equal to the sum of w and 5.

Thus the equation is m = w + 5.

### Page No. 510

Question 9.

The band has a total of 152 members. Some of the members are in the marching band, and the rest are in the concert band. Write an equation that models how many marching band members m there are if there are c concert band members.

Type below:

________________

Answer: m = 152 – c

Explanation:

Given,

The band has a total of 152 members. Some of the members are in the marching band, and the rest are in the concert band.

m is equal to the difference of 152 and c.

The equation is m = 152 – c

Question 11.

Amy volunteers at an animal shelter. She worked 10 hours in March, 12 hours in April, 14 hours in May, and 16 hours in June. If the pattern continues, how many hours will she work in December?

_______ hours

Answer: 28 hours

Explanation:

Amy volunteers at an animal shelter.

She worked 10 hours in March, 12 hours in April, 14 hours in May, and 16 hours in June.

As she started working from the march. December will be the 10th month.

Keep on adding 2 hours for each month you get 28 hours for December.

Thus she worked 28 hours in December.

Question 12.

Aaron wants to buy a new snowboard. The table shows the amount that he has saved. If the pattern in the table continues, how much will he have saved after 1 year?

$ _______

Answer: $540

Explanation:

Aaron wants to buy a new snowboard. The table shows the amount that he has saved.

The equation will be s = 45m

s is the money saved

m is the number of months

1 year = 12 months

s = 45 × 12

s = 540

Thus he saved $540 after 1 year.

### Share and Show – Page No. 513

**Graph the relationship represented by the table.**

Question 1.

Type below:

________________

Answer: y = 50x

Question 2.

Type below:

________________

Answer: y = 5x

**Graph the relationship represented by the table to find the unknown value of y.**

Question 3.

Type below:

________________

Answer: 3

Question 4.

Type below:

________________

Answer: 6

**On Your Own**

**Practice: Copy and Solve Graph the relationship represented by the table to find the unknown value of y.**

Question 5.

Type below:

________________

Answer: 5

Question 6.

Type below:

________________

Answer: 7

### Problem Solving + Applications – Page No. 514

**The table at the right shows the typical price of a popular brand of corn cereal over time. Use the table for 7–8.**

Question 7.

Use Graphs Complete the table below to show the cost of buying 1 to 5 boxes of corn cereal in 1988. Then graph the relationship on the coordinate plane at right.

Type below:

________________

Answer:

Question 8.

Suppose you graphed the cost of buying 1 to 5 boxes of corn cereal using the 1968 price and the 2008 price. Explain how those graphs would compare to the graph you made using the 1988 price.

Type below:

________________

Answer:

The points on both graphs would lie on a line, but the line for the 1968 costs would rise less steeply than the line for 1988 costs and the line for the 2008 costs would rise more steeply than the line for 1988 costs.

Question 10.

Graph the relationship represented by the table to find the unknown value of y.

Type below:

________________

Answer: 3

### Graph Relationships – Page No. 515

**Graph the relationship represented by the table.**

Question 1.

Type below:

________________

Answer: y = 25x

Question 2.

Type below:

________________

Answer:

**Graph the relationship represented by the table to find the unknown value of y.**

Question 3.

Type below:

________________

Answer: 6

Question 4.

Type below:

________________

Answer: 2

**Problem Solving**

Question 5.

Graph the relationship represented by the table.

Type below:

________________

Answer: y = 15x

Question 6.

Use the graph to find the cost of purchasing 5 DVDs.

$ ______

Answer:

The above graph shows that the cost of 5 DVDs is $75.

Question 7.

Both tables and graphs can be used to represent relationships between two variables. Explain how tables and graphs are similar and how they are different.

Type below:

________________

Answer:

Tables and graphs can be useful tools for helping people make decisions. However, they only provide part of a story. Inferences often have to be made from the data shown. As well as being able to identify clearly what the graph or table is telling us, it is important to identify what parts of the story are missing.

### Lesson Check – Page No. 516

Question 1.

Mei wants to graph the relationship represented by the table. Write an ordered pair that is a point on the graph of the relationship.

Type below:

________________

Answer: y = 8x

Question 2.

An online bookstore charges $2 to ship any book. Cole graphs the relationship that gives the total cost y in dollars to buy and ship a book that costs x dollars. Name an ordered pair that is a point on the graph of the relationship.

Type below:

________________

Answer:

An online bookstore charges $2 to ship any book.

Cole graphs the relationship that gives the total cost y in dollars to buy and ship a book that costs x dollars.

y = x + 2

x = 4

y = 4 + 2

y = 6

The ordered pair is (4,6)

**Spiral Review**

Question 3.

Write an expression that is equivalent to 6(g + 4).

Type below:

________________

Answer:

6(g + 4)

6 × g + 6 × 4

6g + 24

Question 5.

Graph n > ^{–}2 on a number line.

Type below:

________________

Answer:

Question 6.

Sam is ordering lunch for the people in his office. The table shows the cost of lunch based on the number of people. How much will lunch cost for 35 people?

$ _____

Answer: 280

Explanation:

Sam is ordering lunch for the people in his office.

The table shows the cost of lunch based on the number of people.

The equation is c = 8n

c = 8 × 35

c = 280

Thus the lunch cost for 35 people is $280.

### Share and Show – Page No. 519

**Graph the linear equation.**

Question 1.

y = x + 2

Type below:

________________

Answer:

Question 2.

y = 3x

Type below:

________________

Answer:

**Write the linear equation for the relationship shown by the graph.**

Question 3.

Type below:

________________

Answer: y = x – 1

Question 4.

Type below:

________________

**On Your Own**

**Graph the linear equation.**

Question 5.

y = x + 1

Type below:

________________

Answer:

Question 6.

y = 2x − 1

Type below:

________________

Answer:

Question 7.

Identify Relationships The graph shows the number of loaves of bread y that Kareem bakes in x hours. Write the linear equation for the relationship shown by the graph.

Type below:

________________

Answer:

The ordered pairs are (1,1), (2,2), (4,4), (5,5)

Look for a pattern among the pairs: each y value is the same as the corresponding x-value.

The equation is y = x

y = x

### Problem Solving + Applications – Page No. 520

**The graph shows the growth of a bamboo plant. Use the graph for 8–9.**

Question 8.

Write a linear equation for the relationship shown by the graph. Use your equation to predict the height of the bamboo plant after 7 days.

Type below:

________________

Answer:

Write the ordered pairs from the graph: (1,50), (2,100), (3,150), (4,200), (5,250).

Look for a pattern among the pairs: each y value is 50 times the corresponding x value.

The equation is y = 50x

For x = 7, the solution is y = 50 × 7 = 350.

So, the height of the bamboo plant after 7 days will be 350 centimeters.

Question 10.

Maria graphed the linear equation y = x + 3. Then she used her ruler to draw a vertical line through the point (4, 0). At what point do the two lines intersect?

Type below:

________________

Answer:

y = x + 3

y = 4 + 0 = 4

y = 4 + 3 = 7

The coordinate is (4, 7)

Question 11.

Antonio claims the linear equation for the relationship shown by the graph is y = \(\frac{1}{2}\)x + 2. Use numbers and words to support Antonio’s claim.

Type below:

________________

Answer:

The ordered pairs (2,3) and (6,5) on the line make the equation.

y = \(\frac{1}{2}\)x + 2

y = 1/2 × 2 + 2

y = 1 + 2 = 3

y = 1/2 × 6 + 2

y = 3 + 2 = 5

### Equations and Graphs – Page No. 521

**Graph the linear equation.**

Question 1.

y = x − 3

Type below:

________________

Answer:

Question 2.

y = x ÷ 3

Type below:

________________

Answer:

**Write a linear equation for the relationship shown by the graph.**

Question 3.

Type below:

________________

Answer:

By seeing the above graph we can say that the equation is

y = x + 1

Question 4.

Type below:

________________

Answer:

The ordered pairs are (1,4), (1.5,6), (2,8)

By seeing the above pairs we can say that the equation is y = 4x

**Problem Solving**

Question 5.

Dee is driving at an average speed of 50 miles per hour. Write a linear equation for the relationship that gives the distance y in miles that Dee drives in x hours.

Type below:

________________

Answer: y = 50x

Explanation:

Dee is driving at an average speed of 50 miles per hour.

y represents the distance in miles

x is the number of hours.

y is equal to the product of 50 and x.

y = 50x

Question 6.

Graph the relationship from Exercise 5.

Type below:

________________

Answer:

Question 7.

Explain how to write a linear equation for a line on a graph.

Type below:

________________

Answer:

To write an equation in slope-intercept form, given a graph of that equation, pick two points on the line and use them to find the slope.

### Lesson Check – Page No. 522

Question 1.

A balloon rises at a rate of 10 feet per second. What is the linear equation for the relationship that gives the height y in feet of the balloon after x seconds?

Type below:

________________

Answer: The linear equation for the relationship is y = 10x

Question 2.

Write the linear equation that is shown by the graph.

Type below:

________________

Answer:

Write the ordered pairs from the graph: (3,3), (5,5), (8,8)

Look for a pattern among the pairs: each y value is the same as the corresponding x-value.

The equation is y = x

**Spiral Review**

Question 4.

Which of the following are solutions of j ≥ 0.6?

j = 1 j = ^{–}0.6 j = \(\frac{3}{5}\) j = 0.12 j = 0.08

Type below:

________________

Answer: j = \(\frac{3}{5}\)

Explanation:

Substitute the values of j in the inequality.

j = 1

1 ≥ 0.6

1 is greater than 0.6 but not equal.

Thus 1 is not the solution of j ≥ 0.6.

j = ^{–}0.6

-0.6 ≥ 0.6

-0.6 is less than 0.6

Thus -0.6 is not the solution of j ≥ 0.6.

j = \(\frac{3}{5}\)

\(\frac{3}{5}\) ≥ 0.6

\(\frac{3}{5}\) = 0.6

0.6 ≥ 0.6

Thus \(\frac{3}{5}\) is the solution.

j = 0.12

0.12 ≥ 0.6

0.12 is less than 0.6.

Thus 0.12 is not the solution of j ≥ 0.6.

j = 0.08

0.08 ≥ 0.6

0.08 is less than 0.6.

Thus 0.08 is not the solution of j ≥ 0.6.

Question 5.

Red grapes cost $2.49 per pound. Write an equation that shows the relationship between the cost c in dollars and the number of pounds of grapes p.

Type below:

________________

Answer: c = 2.49p

Explanation:

Given,

Red grapes cost $2.49 per pound.

c is the cost in dollars.

p is the number of pounds of grapes.

The equation c is equal to the product of the number of pounds of grapes and $2.49

c = 2.49p

### Chapter 9 Review/Test – Page No. 523

Question 1.

A box of peanut butter crackers contains 12 individual snacks. The total number of individual snacks s is equal to 12 times the number of boxes of crackers b.

The independent variable is _____.

The dependent variable is _____.

The equation that represents the relationship between the variables is _____.

Answer:

The independent variable is b.

The dependent variable is s.

The equation that represents the relationship between the variables is s = 12b.

Question 2.

A stationery store charges $8 to print logos on paper purchases. The total cost c is the price of the paper p plus $8 for printing the logo.

For numbers 2a–2d, select True or False for each statement.

2a. The total cost c depends on the price of the paper.

2b. c is the dependent variable.

2c. p is the independent variable.

2d. The equation that represents the relationship between the variables is c = 8p.

2a. ____________

2b. ____________

2c. ____________

2d. ____________

Answer:

2a. True

2b. True

2c. True

2d. False

Explanation:

2a. c represents the relationship between the two quantities.

So, the statement “The total cost c depends on the price of the paper” is true.

2b. c is the total cost so the statement “c is the dependent variable” is true.

2c. p represents the price to print logos

So, the statement “p is the independent variable” is true.

2d. The total cost c is the price of the paper p plus $8 for printing the logo.

The equation would be:

c = 8 + p

Thus the statement “The equation that represents the relationship between the variables is c = 8p” is false.

Question 3.

An electrician charges $75 an hour for labor and an initial fee of $65. The total cost c equals 75 times the number of hours x plus 65. Write an equation for the relationship and use the equation to complete the table.

Type below:

________________

Answer: c = 75x + 65

Substitute the value of x in the equation.

### Page No. 524

Question 4.

The community center offers classes in arts and crafts. There is a registration fee of $125 and each class costs $79. The total cost c in dollars equals 79 times the number of classes n plus 125.

For numbers 4a–4d, select True or False for each statement.

4a. The registration fee is $120.

4b. n is the independent variable.

4c. c is the dependent variable.

4d. The cost for 7 classes is $678.

4a. ____________

4b. ____________

4c. ____________

4d. ____________

Answer:

4a. False

4b. True

4c. True

4d. True

Explanation:

4a. The registration fee is $120.

The registration fee is $125, not $120.

So, the statement is false.

4b. n is the independent variable.

n represents the number of classes.

The statement is true.

4c. c is the dependent variable.

c depends on the registration fee.

Thus the statement is true.

4d. The cost for 7 classes is $678

79 × 7 + 125 = $678

Thus the statement is true.

Question 5.

Ms. Walsh is buying calculators for her class. The table shows the total cost based on the number of calculators purchased.

If Ms. Walsh spent a total of $525, how many calculators did she buy? Use numbers and words to explain your answer.

Type below:

________________

Answer:

She bought 35 calculators. I found a pattern and wrote the equation c = 15n.

Since I know that Mrs.Walsh spent a total of $525, I can substitute 525 for c and solve for n

525 = 15n

n = 35

### Chapter 9 Review/Test – Page No. 525

Question 6.

The table shows the number of cups of lemonade that can be made from cups of lemon juice.

Mary Beth says the number of cups of lemon juice j depends on the number of cups of lemonade l. She says the equation j = 7l represents the relationship between the cups of lemon juice j and the cups of lemonade l. Is Mary Beth correct? Use words and numbers to explain why or why not.

Type below:

________________

Answer:

Mary Beth is not correct. The number of cups of lemonade l depends on the number of cups of lemon juice j.

So l is the dependent variable and j is the independent variable.

The equation showing the relationship is l = 7j

Question 7.

For numbers 7a–7d, choose Yes or No to indicate whether the points, when graphed, would lie on the same line.

7a. (1, 6), (2, 4), (3, 2), (4, 0)

7b. (1, 1), (2, 4), (3, 9), (4, 16)

7c. (1, 3), (2, 5), (3, 7), (4, 9)

7d. (1, 8), (2, 10), (3, 12), (4, 14)

7a. ____________

7b. ____________

7c. ____________

7d. ____________

Answer:

7a. Yes

7b. No

7c. Yes

7d. Yes

Question 8.

Graph the relationship represented by the table to find the unknown value.

Type below:

________________

Answer: 10

### Chapter 9 Review/Test – Page No. 526

Question 9.

Graph the relationship represented by the table.

Type below:

________________

Answer:

Question 10.

Miranda’s wages are $15 per hour. Write a linear equation that gives the wages w in dollars that Miranda earns in h hours.

Type below:

________________

Answer: w = 15h

Question 11.

The table shows the number of miles m that Lucinda could walk in h hours.

Graph the relationship between hours h and miles m. Then write the equation that shows the relationship.

Type below:

________________

Answer: m = 4h

### Chapter 9 Review/Test – Page No. 527

Question 13.

Lacy is staying at a hotel that costs $85 per night. The total cost c in dollars of Lacy’s stay is 85 times the number of nights n she stays.

For numbers, 13a–13d, select True or False for each statement.

13a. The number of nights n is dependent on the cost c.

13b. n is the independent variable.

13c. c is the dependent variable.

13d. The equation that represents the total cost is c = 85n.

13a. ____________

13b. ____________

13c. ____________

13d. ____________

Answer:

13a. False

13b. True

13c. True

13d. True

Explanation:

13a. The number of nights n is dependent on the cost c.

n is independent on the cost c.

So, the statement is false.

13b. n is the independent variable.

The statement is true.

13c. c is the dependent variable.

c is dependent because it depends on the cost c.

So, the statement is true.

13d. The equation that represents the total cost is c = 85n.

The equation is true.

Question 14.

A taxi cab company charges an initial fee of $5 and then $4 per mile for a ride. Use the equation c = 4x + 5 to complete the table.

Type below:

________________

Answer:

Substitute the value of x in the equation.

We get,

### Chapter 9 Review/Test – Page No. 528

Question 15.

A grocery display of cans is arranged in the form of a pyramid with 1 can in the top row, 3 in the second row from the top, 5 in the third row, and 7 in the fourth row. The total number of cans c equals 2 times the row r minus 1. Use the equation c = 2r − 1 to complete the table.

Type below:

________________

Answer:

A grocery display of cans is arranged in the form of a pyramid with 1 can in the top row, 3 in the second row from the top, 5 in the third row, and 7 in the fourth row.

c = 2r − 1

Substitute r in the equation.

Question 16.

The graph shows the number of words Mason read in a given amount of minutes. If Mason continues to read at the same rate, how many words will he have read in 5 minutes?

______ words

Answer: 1000 words

By seeing the above graph we can say that Mason can read 1000 words in 5 minutes.

Question 17.

Casey claims the linear equation for the relationship shown by the graph is c = 25j. Use numbers and words to support Casey’s claim.

Type below:

________________

Answer: The ordered pairs (1,25), (3,75), (5,125) and (7,175) each make the equation c = 25j

*Conclusion:*

I wish the details prevailed in the Go Math Grade 6 Answer Key Chapter 9 is helpful for you. Share this pdf link with your friends and help them to overcome the difficulties. If you have any doubts regarding the solutions you can leave a comment in the comment section.

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