Linear Functions Formative 2

1) Check all of the linear equations.

A

B

C

D

E

F

The correct answer includes options A, C, and D. This means that these options are the linear equations among the given choices. The other options, B, E, and F, are not linear equations.

Explanation

The correct answer includes options A, C, and D. This means that these options are the linear equations among the given choices. The other options, B, E, and F, are not linear equations.

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2) Check all of the non-linear equations.

A

B

C

D

E

F

The correct answer includes options B, E, and F. These options are considered non-linear equations because they do not follow a straight line when graphed. Option A, C, and D are not non-linear equations as they represent linear equations that can be graphed as straight lines.

Explanation

The correct answer includes options B, E, and F. These options are considered non-linear equations because they do not follow a straight line when graphed. Option A, C, and D are not non-linear equations as they represent linear equations that can be graphed as straight lines.

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3) Check all of the equations with a rate of change of 5.

A

B

C

D

E

F

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Explanation

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4) Joanna purchased a house for $200,000. Each year the value of her house increases by 3%. Does this model a linear relationship?

Yes

No

The given scenario does not model a linear relationship because a linear relationship implies that the value of the house would increase by a constant amount each year. However, in this case, the value of the house increases by a percentage (3%) each year, which means that the increase is not constant but rather proportional to the current value of the house. Therefore, it does not follow a linear pattern.

Explanation

The given scenario does not model a linear relationship because a linear relationship implies that the value of the house would increase by a constant amount each year. However, in this case, the value of the house increases by a percentage (3%) each year, which means that the increase is not constant but rather proportional to the current value of the house. Therefore, it does not follow a linear pattern.

5) About how much will Joanna's house be worth after the third year?

$218,000

$439,400

$218,550

$219,450

Based on the given options, it can be inferred that the value of Joanna's house will increase over time. Among the options, the closest value to the initial worth of the house ($218,000) is $218,550. This suggests that after the third year, the value of Joanna's house will increase by $550, resulting in a worth of $218,550.

Explanation

Based on the given options, it can be inferred that the value of Joanna's house will increase over time. Among the options, the closest value to the initial worth of the house ($218,000) is $218,550. This suggests that after the third year, the value of Joanna's house will increase by $550, resulting in a worth of $218,550.

6) Choose one.

Both graphs are always increasing.

Both graphs are always decreasing.

Graph A is always increasing and Graph B is not.

Graph B is always increasing and Graph A is not.

The given answer states that Graph B is always increasing and Graph A is not. This means that the values of Graph B consistently increase as the independent variable increases, while the values of Graph A do not follow a consistent upward trend.

Explanation

The given answer states that Graph B is always increasing and Graph A is not. This means that the values of Graph B consistently increase as the independent variable increases, while the values of Graph A do not follow a consistent upward trend.

7) Choose one.

-2

-5

2

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Explanation

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8) Choose one.

Both graphs change in a linear pattern.

Neither graph changes in a linear pattern.

Graph A is linear and Graph B is non-linear.

Graph A is non-linear and Graph B is linear.

The explanation for the correct answer is that a linear pattern is characterized by a constant rate of change, where the values increase or decrease at a consistent rate. In Graph A, the values do not follow a consistent rate of change, indicating a non-linear pattern. On the other hand, Graph B shows a consistent rate of change, which suggests a linear pattern. Therefore, the correct answer is that Graph A is non-linear and Graph B is linear.

Explanation

The explanation for the correct answer is that a linear pattern is characterized by a constant rate of change, where the values increase or decrease at a consistent rate. In Graph A, the values do not follow a consistent rate of change, indicating a non-linear pattern. On the other hand, Graph B shows a consistent rate of change, which suggests a linear pattern. Therefore, the correct answer is that Graph A is non-linear and Graph B is linear.

9) Joe just got a job at Little Caesar's. He will be making $8.00 per hour and he has to pay for his uniform which cost $24.99. Does this represent a linear relationship?

Yes

No

Yes, this represents a linear relationship because Joe's hourly wage is constant at $8.00 per hour and the cost of his uniform is a fixed amount of $24.99. Linear relationships involve a constant rate of change, and in this case, the rate of change is $8.00 per hour for Joe's wage and $0.00 per hour for the cost of his uniform.

Explanation

Yes, this represents a linear relationship because Joe's hourly wage is constant at $8.00 per hour and the cost of his uniform is a fixed amount of $24.99. Linear relationships involve a constant rate of change, and in this case, the rate of change is $8.00 per hour for Joe's wage and $0.00 per hour for the cost of his uniform.

10) If possible, predict how many hours will Joe need to work to make more than $150?

19

20

21

22

Joe will need to work for 22 hours in order to make more than $150. This can be inferred because the question asks how many hours Joe needs to work to make more than $150, and the answer given is 22.

Explanation

Joe will need to work for 22 hours in order to make more than $150. This can be inferred because the question asks how many hours Joe needs to work to make more than $150, and the answer given is 22.

11) In 2002, there were 520 fish in a pond. In 2005, there were 580 fish in the same pond. In 2008, there were 640 fish in the pond. Does the number of fish in the pond per year model a linear relationship?

Yes

No

The given data shows an increase in the number of fish in the pond over time. In 2002, there were 520 fish, in 2005 there were 580 fish, and in 2008 there were 640 fish. The increase in the number of fish per year is consistent, with an increase of 60 fish between 2002 and 2005, and another increase of 60 fish between 2005 and 2008. This consistent increase suggests a linear relationship, where the number of fish in the pond per year can be modeled by a straight line. Therefore, the answer is yes.

Explanation

The given data shows an increase in the number of fish in the pond over time. In 2002, there were 520 fish, in 2005 there were 580 fish, and in 2008 there were 640 fish. The increase in the number of fish per year is consistent, with an increase of 60 fish between 2002 and 2005, and another increase of 60 fish between 2005 and 2008. This consistent increase suggests a linear relationship, where the number of fish in the pond per year can be modeled by a straight line. Therefore, the answer is yes.

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13) Your conducting a biology experiment. At the beginning of the experiment you have 5 cells. Each day, you notice that the number of cells in your sample is doubling. Does this represent a linear relationship?

Yes

No

No, the relationship does not represent a linear relationship. In a linear relationship, the change in one variable is proportional to the change in another variable. However, in this case, the number of cells is doubling each day, which means the relationship is exponential. The number of cells is increasing at an increasing rate, not a constant rate.

Explanation

No, the relationship does not represent a linear relationship. In a linear relationship, the change in one variable is proportional to the change in another variable. However, in this case, the number of cells is doubling each day, which means the relationship is exponential. The number of cells is increasing at an increasing rate, not a constant rate.

14) Check all that apply.

The rate of change for Table A is 3.

The rate of change for Table A is 4

The rate of change for Table B is .

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Explanation

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15) Choose one.

Both tables are increasing.

Both tables are decreasing.

Table A is decreasing and Table B is not.

Table A is increasing and Table B is not.

This answer suggests that Table A is showing an upward trend, with values increasing over time, while Table B does not exhibit any consistent trend and may have values that fluctuate or remain constant.

Explanation

This answer suggests that Table A is showing an upward trend, with values increasing over time, while Table B does not exhibit any consistent trend and may have values that fluctuate or remain constant.

16) Choose one.

Both tables have a constant rate of change.

Neither table has a constant rate of change.

Table A has a constant rate of change.

Table B has a constant rate of change.

The answer is Table B has a constant rate of change because the values in Table B increase or decrease by the same amount for each corresponding input value. This indicates that there is a consistent and constant rate of change between the input and output values in Table B.

Explanation

The answer is Table B has a constant rate of change because the values in Table B increase or decrease by the same amount for each corresponding input value. This indicates that there is a consistent and constant rate of change between the input and output values in Table B.