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. (2 points)
Hours: 1, 2, 3, 4
Money: 9, 18, 27, 36
To determine if the data table represents a proportional relationship, we need to check if the ratio of the quantities remains the same.
Let's calculate the ratio of money to hours for each combination in the table:
For the first combination: 9/1 = 9
For the second combination: 18/2 = 9
For the third combination: 27/3 = 9
For the fourth combination: 36/4 = 9
As we can see, the ratio of money to hours is consistently 9 for all combinations. This means that for every hour worked, the amount of money earned is always 9.
Since the ratio of the quantities remains constant, we can conclude that the data table represents a proportional relationship.
wrong my teacher says i googled my answer
My apologies for any confusion. I am an AI language model and do not have the ability to access or search the internet. However, based on the data provided in the table, I can still determine if it represents a proportional relationship.
To check for proportionality, we need to see if the ratio of money to hours is constant throughout the table. Let's calculate the ratio for each combination:
1st combination: 9/1 = 9
2nd combination: 18/2 = 9
3rd combination: 27/3 = 9
4th combination: 36/4 = 9
As we can see, the ratio of money to hours is consistently 9 for all combinations. This indicates that for every additional hour, the amount of money earned increases by a constant rate of 9.
Therefore, based on the calculations, the table represents a proportional relationship.
To determine if the table represents a proportional relationship, we need to check if the ratio between the quantities in the first column (hours) and the second column (money) remains constant.
We can calculate the ratio for each pair of values by dividing the money value by the corresponding hours value.
For the given data table:
- To calculate the ratio for the first pair, we divide 9 (money) by 1 (hours): 9/1 = 9.
- For the second pair, we divide 18 (money) by 2 (hours): 18/2 = 9.
- For the third pair, we divide 27 (money) by 3 (hours): 27/3 = 9.
- For the fourth pair, we divide 36 (money) by 4 (hours): 36/4 = 9.
As shown, the ratio between the money and hours values is constant at 9. This indicates that the table represents a proportional relationship because the ratio remains the same for each pair of values.
To summarize, I determined that the table represents a proportional relationship by calculating the ratio between the money and hours values for each pair of values. The resulting ratios were all equal to 9, indicating a constant ratio and therefore a proportional relationship.