Respuesta :
Answer:
D. y = 64 + 22x
Step-by-step explanation:
To determine the most appropriate equation for modeling the given data, we need to analyze the pattern and relationship between the x-values (123456) and y-values (79 101 124 158 195 244).
Observing the data points, we can see that the y-values are increasing in a non-linear pattern as x increases. Let's calculate the differences between consecutive y-values to identify the pattern:
101 - 79 = 22
124 - 101 = 23
158 - 124 = 34
195 - 158 = 37
244 - 195 = 49
From the differences, we can observe that the increments are not consistent, indicating a non-linear relationship. Therefore, options A and B, which have constant increments (1.25), do not match the data pattern.
Now, let's evaluate the remaining options:
C. y = 79 + 1.25x
This equation includes a constant term (79) and a linear term (1.25x). However, as the relationship between x and y seems more complex than a simple linear one, this equation may not capture the pattern accurately.
D. y = 64 + 22x
This equation includes a constant term (64) and a linear term (22x) that align with the observed differences between y-values. The increments between consecutive y-values match the pattern seen in the data (22, 23, 34, 37, 49). Therefore, option D is the most appropriate equation for modeling this data as it reflects the non-linear relationship between x and y values observed in the given dataset.
