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?
answers:
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.
To determine the relationship between the values of x and y in the table, let's analyze the given options:
A: 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.
C: Danee had eight dance classes per week.
D: Yolanda had eight books and bought one new book each week.
Looking at the table, we can see that as the value of x increases by 1 (from 0 to 3), the value of y also increases by 1 (from 8 to 11). This means that there is a constant rate of change between the values of x and y.
Option A describes a situation where the rate of change is not constant. Option B also does not have a constant rate of change, as the number of fish caught increases by 8 each minute, not by 1.
Option C describes a different situation where the value of y remains constant, while x increases. This does not match the table's values.
Option D describes a situation where there is a constant rate of change, as Yolanda buys one new book each week. However, the starting value of y is already 8 (not 0), which does not match the table's values.
Therefore, the situation that best describes the relationship between all the values of x and y in the table is option D: Yolanda had eight books and bought one new book each week.
To determine which situation best describes the relationship between the values of x and y in the table, we need to first understand the pattern between them.
Looking at the table:
x: 0 1 2 3
y: 8 9 10 11
We can observe that as x increases by 1, y also increases by 1. This means that for each increment of x, there is a corresponding increment of y.
Now, let's examine each answer option and determine which one aligns with this pattern:
A: Lincoln started with zero stamps in his collection for the first 8 months and then started to collect one stamp per month.
This option does not align with the pattern between x and y in the table. In this situation, the number of stamps collected does not increase by 1 for each increment of 1 for x.
B: Gavin caught one fish in the first minute of fishing and eight fish each minute after.
This option also does not align with the pattern. The number of fish caught does not increase by 1 for each increment of 1 for x.
C: Danee had eight dance classes per week.
This option does not align with the pattern either. The number of dance classes per week does not increase by 1 for each increment of 1 for x.
D: Yolanda had eight books and bought one new book each week.
This option aligns with the pattern. Yolanda starts with 8 books and then buys 1 new book each week, resulting in an increase of 1 for each increment of 1 for x.
Based on the pattern and the options provided, the situation that best describes the relationship between all the values of x and y in the table is option D: Yolanda had eight books and bought one new book each week.