ric has $27.00 and wants to buy comic books. If each comic book costs $4.00, create a table and graph the arithmetic sequence to display how much money Eric has left after each comic book purchase. Which graph is an accurate representation of the problem?

Answer 1

To create a table and graph for Eric's comic book purchases, let’s first calculate how much money he has left after each purchase.

Eric starts with $27.00 and spends $4.00 on each comic book. We can set up the following sequence for the number of comic books purchased (0, 1, 2, 3, ...) and the corresponding amount of money left after each purchase.

Table of Money Left After Each Comic Book Purchase

| Comic Books Purchased | Money Spent | Money Left | |-----------------------|-------------|------------| | 0 | $0.00 | $27.00 | | 1 | $4.00 | $23.00 | | 2 | $8.00 | $19.00 | | 3 | $12.00 | $15.00 | | 4 | $16.00 | $11.00 | | 5 | $20.00 | $7.00 | | 6 | $24.00 | $3.00 | | 7 | $28.00 | -$1.00 |

Note: After purchasing 6 comic books, Eric will have $3.00 left. By the time he tries to buy a 7th comic book, he doesn't have enough money, leading to a negative balance, which indicates he can't afford more.

Graphing the Money Left

To display this data graphically, you can plot the number of comic books purchased on the x-axis and the money left on the y-axis:

• X-axis: Number of Comic Books Purchased
• Y-axis: Money Left

Here's the data we'll plot:

• (0, 27)
• (1, 23)
• (2, 19)
• (3, 15)
• (4, 11)
• (5, 7)
• (6, 3)
• (7, -1)

Description of the Graph

The graph will show a downward trend that starts at $27.00 when no comic books are purchased and decreases steadily until it hits $0.00 at the 6th book, after which it dips into the negative on the 7th book.

The graph should be a straight line decreasing with a slope corresponding to the cost of the comic books.

Choosing Accurate Graph Representation

A graph representing this scenario would be a linear graph that decreases from (0, 27) to (6, 3), followed by a line extending into the negative region for (7, -1).

If you have options for different graphs provided to you, look for:

1. A straight line from $27 down to $3.
2. It should go through the points correctly, indicating that at 6 comic books he has $3 left and at 7 comic books, it's below $0.

This graph visually illustrates the relationship between the number of comic books bought and the money left.