Mr. Kelly gives his favorite kid an allowance. The graphs shows how much his favorite kid earns over time. a. Find the constant of proportionality. \( k= \) b. Use a sentence to explain what the constant of proportionality means in this situation. c. Write an equation to represent the relationship between the amount of time and money earned. d. Explain what the point (4,30) means in this situation.

Sure, let's work through each part of the problem step by step. Since the graph isn't provided, we'll base our solutions on the information given, particularly the point \((4, 30)\). ### a. Find the constant of proportionality. \( k = \) **Solution:** The constant of proportionality \( k \) represents the rate at which the money earned changes with respect to time. From the point \((4, 30)\), we can determine \( k \) by dividing the amount earned by the time taken. \[ k = \frac{\text{Amount Earned}}{\text{Time}} = \frac{30}{4} = 7.5 \] **Answer:** \[ k = 7.5 \] --- ### b. Use a sentence to explain what the constant of proportionality means in this situation. **Answer:** The constant of proportionality \( k = 7.5 \) means that Mr. Kelly’s favorite kid earns \$7.50 for each unit of time (for example, each hour) they spend working. --- ### c. Write an equation to represent the relationship between the amount of time and money earned. **Solution:** Since the relationship is proportional, it can be represented by a linear equation passing through the origin. Let \( t \) represent time and \( m \) represent money earned. \[ m = k \cdot t \] Substituting \( k = 7.5 \): \[ m = 7.5t \] **Answer:** \[ m = 7.5\, t \] --- ### d. Explain what the point \((4, 30)\) means in this situation. **Answer:** The point \((4, 30)\) indicates that after 4 units of time (for example, 4 hours), Mr. Kelly’s favorite kid has earned \$30.