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.
Hours Money (S)
1. 9
2. 18
3. 27
4. 36
(2 points)
To determine if the table represents a proportional relationship, we need to check if the ratio between the hours and money remains constant.
Let's calculate the ratios between hours and money:
1 hour corresponds to 9 units of money
2 hours correspond to 18 units of money
3 hours correspond to 27 units of money
4 hours correspond to 36 units of money
Dividing the units of money by the corresponding number of hours for each observation, we get:
1st observation: 9 units of money ÷ 1 hour = 9 units of money/hour
2nd observation: 18 units of money ÷ 2 hours = 9 units of money/hour
3rd observation: 27 units of money ÷ 3 hours = 9 units of money/hour
4th observation: 36 units of money ÷ 4 hours = 9 units of money/hour
As we can see, the ratio between hours and money is consistently 9 units of money for each hour. This means that the table represents a proportional relationship because the ratio remains constant.