Mrs. Smith asked her students to write a situation that could describe the relationship between all of the values of x and y in the table.
x
0 1 2 3
y 8 9 10 11
Which situation best describes the relationship between all the values of x and y in the table?
Responses
A Lincoln started with zero stamps in his collection for the first 8 months and then started to collect one stamp per month.Lincoln started with zero stamps in his collection for the first 8 months and then started to collect one stamp per month.
B Gavin caught one fish in the first minute of fishing and eight fish each minute after.Gavin caught one fish in the first minute of fishing and eight fish each minute after.
C Danee had eight dance classes per week.Danee had eight dance classes per week.
D Yolanda had eight books and bought one new book each week.
The situation that best describes the relationship between all the values of x and y in the table is D. Yolanda had eight books and bought one new book each week.
Based on the table, the situation that best describes the relationship between all the values of x and y is D - Yolanda had eight books and bought one new book each week. In the table, as x increases by 1 (from 0 to 1, 1 to 2, and so on), y also increases by 1 (from 8 to 9, 9 to 10, and so on). This represents a linear relationship between x and y.
To determine which situation best describes the relationship between all the values of x and y in the table, we need to analyze the values in both the x and y columns.
Looking at the x column, we see that the values are increasing by 1 each time: 0, 1, 2, 3. This indicates a pattern of adding 1 each time.
Looking at the y column, we see that the values are also increasing by 1 each time: 8, 9, 10, 11. This indicates a pattern of adding 1 each time, similar to the x column.
Based on this analysis, we can conclude that the best description for the relationship between all the values of x and y in the table is a situation where there is a consistent increase of 1.
Now let's look at the options:
A. Lincoln started with zero stamps in his collection for the first 8 months and then started to collect one stamp per month. This situation matches our analysis as the values in the y column also increase by 1 each time.
B. Gavin caught one fish in the first minute of fishing and eight fish each minute after. This situation does not match our analysis as the values in the y column are increasing by 8 each time, not 1.
C. Danee had eight dance classes per week. This situation does not match our analysis as the values in the y column are increasing by 1 each time, not 8.
D. Yolanda had eight books and bought one new book each week. This situation does not match our analysis as the values in the y column are increasing by 1 each time, not 8.
Therefore, the situation that best describes the relationship between all the values of x and y in the table is option A: Lincoln started with zero stamps in his collection for the first 8 months and then started to collect one stamp per month.