Question

Samantha’s parents give her $10 per week. For each chore that she does not complete, she must repay her parents $1. Which graph models Samantha’s allowance?
A graph titled Samantha's Allowance has chores not completed on the x-axis and amount earned on the y-axis. A line goes through points (0, 10) and (1, 9).
A graph titled Samantha's Allowance has chores not completed on the x-axis and amount earned on the y-axis. A line goes through points (0, 10) and (2, 12).
A graph titled Samantha's Allowance has chores not completed on the x-axis and amount earned on the y-axis. A line goes through points (1, 6) and (1.5, 16).
A graph titled Samantha's Allowance has chores not completed on the x-axis and amount earned on the y-axis. A line goes through points (0, 10) and (1, 0).

Answer 1

To model Samantha's allowance, we need to understand how her earnings change based on the number of chores not completed.

1. Samantha starts with a base allowance of $10 each week.
2. For each chore not completed, she loses $1.

This means her amount earned (y-axis) will decrease by $1 for every chore not completed (x-axis). Thus, the relationship can be represented as:

- If no chores are missed (0 chores not completed), she earns $10.
- If 1 chore is not completed, she earns $10 - $1 = $9.
- If 2 chores are not completed, she earns $10 - $2 = $8, and so on.

Now, we look at the given options:

1. **First option**: A line through points (0, 10) and (1, 9). This indicates that when 0 chores are completed, she has $10, and when 1 chore is not completed, she has $9. This correctly models the scenario since each missed chore deducts $1 from her allowance.

2. **Second option**: A line through points (0, 10) and (2, 12). This incorrectly suggests that her allowance increases with the number of chores not completed, which does not make sense.

3. **Third option**: A line through points (1, 6) and (1.5, 16). This relationship does not accurately reflect the linear deduction based on chores not completed.

4. **Fourth option**: A line through points (0, 10) and (1, 0). This suggests that after missing just one chore, her allowance drops to $0. This would imply she owes her parents $10, which isn’t consistent with her losing $1 for each chore.

The correct graph that models Samantha's allowance is the **first option**, which accurately depicts her allowance decreasing by $1 for each chore she fails to complete.