Two students are earning money. Student A earns $5 for each chore that is completed. Student B earns a weekly allowance of $10 with $5 for each chore that is completed. Which of their situations show a linear relationship that is also proportional?

1 answer

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.