Proportional Relationships in Tables Quick Check
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Question
Use the table to answer the question.
Time (min) 1 2 3 7 10
Water Used (gal) 5 10 15 35 50
Determine if the quantities in the data table re in a proportional relationship. If they do not have a proportional relationship, indicate why.
(1 point)
Responses
Yes, the data table has a proportional relationship.
Yes, the data table has a proportional relationship.
No, the ratios are not equivalent.
No, the ratios are not equivalent.
No, the table does not count consecutively.
No, the table does not count consecutively.
No, the ratio 7:35 is not proportional to the other ratios.
No, the ratio ratio of 7 to 35 is not proportional to the other ratios.
No, the ratios are not equivalent.
To determine if the quantities in the data table are in a proportional relationship, we need to compare the ratios of water used to time for each pair of values.
If the ratios are equivalent for all pairs, then the data table has a proportional relationship. However, if any of the ratios are not equal, then the data table does not have a proportional relationship.
Let's calculate the ratios:
For time 1 and water used 5, the ratio is 5/1 = 5.
For time 2 and water used 10, the ratio is 10/2 = 5.
For time 3 and water used 15, the ratio is 15/3 = 5.
For time 7 and water used 35, the ratio is 35/7 = 5.
For time 10 and water used 50, the ratio is 50/10 = 5.
Since all the ratios are equal (5), the data table has a proportional relationship.
Therefore, the correct response is:
Yes, the data table has a proportional relationship.
To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratios between the values in the "Time (min)" column and the "Water Used (gal)" column are consistent.
We can start by calculating the ratios for each pair of values. For example, the ratio for the first pair (1 min and 5 gal) is 1:5. Similarly, for the second pair (2 min and 10 gal), the ratio is 2:10, which simplifies to 1:5 as well. We can continue this process for all the pairs:
1:5
2:10 (1:5)
3:15 (1:5)
7:35 (1:5)
10:50 (1:5)
As we can see, the ratios for all pairs are equivalent to 1:5. This means that the ratios are consistent, and therefore, the quantities in the data table have a proportional relationship.
Therefore, the correct response is:
Yes, the data table has a proportional relationship.