To determine which student's situation shows a linear relationship that is also proportional, we need to analyze their earnings in relation to the number of chores completed.
Student A:
- Earnings: $5 per chore
- The relationship can be described using the equation \( y = 5x \), where \( y \) is the total earnings and \( x \) is the number of chores completed.
- This situation is linear and passes through the origin (0,0), which means it is proportional.
Student B:
- Earnings: $10 weekly allowance + $5 per chore
- The relationship can be described using the equation \( y = 10 + 5x \).
- This situation is linear, but it does not pass through the origin because when \( x = 0 \), \( y = 10 \). Therefore, it is not proportional.
Conclusion: Student A's earnings represent a linear relationship that is also proportional, while Student B's situation represents a linear relationship but is not proportional due to the presence of the fixed allowance.