A store sells packages of comic books with a poster. A poster and 6 comics cost $12.75. A poster and 15 comics cost $21.75. Write a linear function rule that models the cost y of a package containing any number x of comic books.
Suppose another store sells a similar package, modeled by a linear function rule with initial value $7.99. Use pencil and paper. Explain which store has the better deal

To write a linear function rule that models the cost y of a package containing any number x of comic books, we can first find the cost for a poster and 6 comics and the cost for a poster and 15 comics. Then, we can determine the slope (rate of change) and the y-intercept (initial value).

Given:

- A poster and 6 comics cost $12.75

- A poster and 15 comics cost $21.75

To find the linear function rule:

1. Determine the cost for the comics in each package:

- For the first package (poster + 6 comics):

12.75 - cost of the poster = cost of 6 comics

- For the second package (poster + 15 comics):

21.75 - cost of the poster = cost of 15 comics

2. Find the cost of the poster by subtracting the cost of the comics from the total cost:

- For the first package:

Cost of the poster = 12.75 - cost of 6 comics

- For the second package:

Cost of the poster = 21.75 - cost of 15 comics

3. Determine the cost of one comic book by dividing the cost of the comics by the number of comics:

- For the first package:

Cost of one comic book = Cost of 6 comics / 6

- For the second package:

Cost of one comic book = Cost of 15 comics / 15

4. Write the linear function rule:

- Let y be the total cost of the package and x be the number of comic books.

- The linear function rule will have the form: y = mx + b, where m is the cost of one comic book and b is the cost of the poster.

After finding the linear function rule for both stores, compare the slopes (cost of one comic book) and y-intercepts (cost of the poster) to determine which store offers the better deal based on the cost per comic book and the initial cost of the package.