The data (1,5), (3,16), (5,35), (7,67), (9,110) could be modeled as a linear relationship if
If the data points can be modeled as a linear relationship, it means that they can be plotted on a graph such that they lie on a straight line. To verify if this is the case, we can calculate the slope between each pair of consecutive points and check if the slopes are approximately equal.
Let's calculate the slopes between each pair of consecutive points:
Slope between (1,5) and (3,16):
slope = (16 - 5) / (3 - 1) = 11 / 2 = 5.5
Slope between (3,16) and (5,35):
slope = (35 - 16) / (5 - 3) = 19 / 2 = 9.5
Slope between (5,35) and (7,67):
slope = (67 - 35) / (7 - 5) = 32 / 2 = 16
Slope between (7,67) and (9,110):
slope = (110 - 67) / (9 - 7) = 43 / 2 = 21.5
Since the slopes are not approximately equal, we can conclude that the data points do not form a linear relationship. Therefore, the given data cannot be modeled as a linear relationship.