The quantities in the data table are in a proportional relationship. Using the data in the table, show your work and explain how you know the table represents a proportional relationship

Question

Hours Money ($)
1. 9
2. 18
3. 27
4. 36

Answer 1

To determine if the table represents a proportional relationship, we need to check if there is a constant ratio between the hours and money.

First, we can check if the money values increased by a consistent amount for each additional hour. Dividing the money value for any two consecutive hours should yield the same result if the relationship is proportional.

18 ÷ 9 = 2
27 ÷ 18 = 1.5
36 ÷ 27 = 1.333...

Since the quotient does not remain constant, it suggests that the relationship may not be proportional. However, to confirm this, we should also consider if the hours values increased by a consistent amount for each additional hour.

2 - 1 = 1
3 - 2 = 1
4 - 3 = 1

The difference between the hours values remains constant at 1 for each additional hour. This implies that the relationship is indeed proportional.

So, while the money values do not increase at a constant rate, the hours values increase by a constant value for every additional hour. This confirms that the table represents a proportional relationship.