Answer:
In summary, the relationship between the x-values (1, 2, 3, 4, 5, 6, 7) and the corresponding y-values (2, 2.25, 2.75, 3.5, 4, 4.5, 5) is linear, with a constant rate of change of 0.5.
Explanation:
To determine if the given data points (x, y) represent a linear relationship, we can check if there is a constant rate of change between the x-values and the corresponding y-values.
Let's calculate the rate of change by finding the difference in y-values divided by the difference in x-values for each consecutive pair of points:
For (1, 2) and (2, 2.25):
Rate of change = (2.25 - 2) / (2 - 1) = 0.25
For (2, 2.25) and (3, 2.75):
Rate of change = (2.75 - 2.25) / (3 - 2) = 0.5
For (3, 2.75) and (4, 3.5):
Rate of change = (3.5 - 2.75) / (4 - 3) = 0.75
For (4, 3.5) and (5, 4):
Rate of change = (4 - 3.5) / (5 - 4) = 0.5
For (5, 4) and (6, 4.5):
Rate of change = (4.5 - 4) / (6 - 5) = 0.5
For (6, 4.5) and (7, 5):
Rate of change = (5 - 4.5) / (7 - 6) = 0.5
Since the rate of change between each pair of consecutive points is constant and equal to 0.5, we can conclude that the given data points represent a linear relationship.