Question

he quantities in the data table are in a proportional relationship. Using the data in the table, show your work and explain how you know the table represents a proportional relationship.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine if the data table represents a proportional relationship, we need to check if the ratio between each pair of values remains constant.

Let's take the first row of the table as an example:

x | y
-----
1 | 2
2 | 4
3 | 6

To check if the relationship is proportional, we can calculate the ratio of y to x for each pair of values:

2/1 = 2
4/2 = 2
6/3 = 2

As we can see, the ratio stays constant at 2 for each pair of values. This indicates that there is a proportional relationship between x and y in the first row of the table.

We can repeat the same process for the rest of the rows in the table to check if the ratio remains constant. If the ratio does remain constant for each pair of values throughout the table, then it represents a proportional relationship.

Answer 2

It takes Julian 12 hour to walk 2 miles. He decides to start working in his spare time, but because he wants to make sure he has enough time to go a desired distance he created the data table. At which ratio does the constant of proportionality appear?

(1 point)
Responses

(14,1)open paren 1 fourth comma 1 close paren

(4, 1)
(4, 1)

(1, 4)
(1, 4)

(1,14)open paren 1 comma 1 fourth close paren

Answer 3

[AI-generated answer — Bot GPT 3.5]

To determine the ratio at which the constant of proportionality appears, we can analyze the data in the table.

If we label the time (in hours) as x and the distance (in miles) as y, the data table is as follows:

x | y
-----
12 | 2
6 | 1
3 | 1/2
1.5 | 1/4

To find the ratio at which the constant of proportionality appears, we can calculate the ratio of y to x for each pair of values:

2/12 = 1/6
1/6 = 1/6
1/2 /3 = 1/6
1/4 /1.5 = 1/6

From the calculations, it is evident that the ratio of 1/6 remains constant for each pair of values. Therefore, the constant of proportionality appears at the ratio (1/6).

So the correct answer is: (1/6).

Answer 4

It takes Julian 1/2 hour to walk 2 miles. He decides to start working in his spare time, but because he wants to make sure he has enough time to go a desired distance he created the data table. At which ratio does the constant of proportionality appear?

(1 point)
Responses

(1/4,1)open paren 1 fourth comma 1 close paren

(4, 1)
(4, 1)

(1, 4)
(1, 4)

(1,1/4)open paren 1 comma 1 fourth close paren

Answer 5

[AI-generated answer — Bot GPT 3.5]

To determine the ratio at which the constant of proportionality appears, we can analyze the data in the table.

If we label the time (in hours) as x and the distance (in miles) as y, the data table is as follows:

x | y
-----
1/2 | 2
1/4 | 1
1/8 | 1/2
1/16 | 1/4

To find the ratio at which the constant of proportionality appears, we can calculate the ratio of y to x for each pair of values:

2 / (1/2) = 4
1 / (1/4) = 4
1/2 / (1/8) = 4
1/4 / (1/16) = 4

From the calculations, it is evident that the ratio of 4 remains constant for each pair of values. Therefore, the constant of proportionality appears at the ratio (4).

So the correct answer is: (4).

Answer 6

Ruth can read 15 pages in 30 minutes. She decides to create a table to keep track of her progress. From the data provided, at what ratio is the unit rate (constant of proportionality) represented?

(1 point)
Responses

(2, 60)
(2, 60)

(1, 30)
(1, 30)

(1/2, 15)(12, 15)

(15, 30)
(15, 30)
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Answer 7

[AI-generated answer — Bot GPT 3.5]

To determine the ratio at which the unit rate (constant of proportionality) is represented, we need to analyze the given data.

If we label the number of pages as x and the time (in minutes) as y, the data provided is as follows:

x | y
-----
15 | 30

To find the ratio at which the unit rate is represented, we can calculate the ratio of x to y:

15 / 30 = 1/2

From the calculation, we can see that the ratio 1/2 represents the unit rate or constant of proportionality.

So the correct answer is: (1/2, 15).