Final answer:
The function representing the length of the vine after n weeks is L = 9 + 1.5n, where L is the length of the vine and n is the number of weeks.
Step-by-step explanation:
The length of a vine after n weeks can be represented by a linear function. Since the vine is initially 9 inches long and grows at a rate of 1.5 inches per week, we can create the function based on the starting length and the growth rate. The function that represents the length of the vine (L) after n weeks (n being the number of weeks) is:
L = 9 + 1.5n
In this function, 9 is the initial length of the vine in inches, and 1.5n represents the total growth over n weeks, with 1.5 indicating the growth per week and n representing the number of weeks.