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 -
1.
2.
3.
4.
Money -
9.
18.
27.
36.
To determine if the table represents a proportional relationship, we need to check if the ratio of hours to money is constant.
The ratio of hours to money in this table is:
1 hour = $9
2 hours = $18
3 hours = $27
4 hours = $36
To find the ratio, we divide the money by the corresponding hours:
$9 / 1 hour = $9/hour
$18 / 2 hours = $9/hour
$27 / 3 hours = $9/hour
$36 / 4 hours = $9/hour
We can see that the ratio of money to hours is consistently $9 per hour. This means that for every hour worked, the person earns $9, and the relationship between the hours and money is proportional.
can you make it step by step
Certainly! Here are the step-by-step calculations:
Step 1: Calculate the ratio for the first row:
- Hours: 1
- Money: 9
Ratio: 9/1 = 9
Step 2: Calculate the ratio for the second row:
- Hours: 2
- Money: 18
Ratio: 18/2 = 9
Step 3: Calculate the ratio for the third row:
- Hours: 3
- Money: 27
Ratio: 27/3 = 9
Step 4: Calculate the ratio for the fourth row:
- Hours: 4
- Money: 36
Ratio: 36/4 = 9
In each step, we divide the money by the corresponding number of hours. We can see that in all four calculations, the ratio is 9. This demonstrates that the relationship between the hours and money in this table is proportional.
To determine if the data table represents a proportional relationship, we need to check if there is a constant ratio between the Hours and Money columns.
To do this, let's calculate the ratios between Hours and Money for each row in the table.
For the first row:
Hours = 1
Money = 9
Ratio = Money / Hours = 9 / 1 = 9
For the second row:
Hours = 2
Money = 18
Ratio = Money / Hours = 18 / 2 = 9
For the third row:
Hours = 3
Money = 27
Ratio = Money / Hours = 27 / 3 = 9
For the fourth row:
Hours = 4
Money = 36
Ratio = Money / Hours = 36 / 4 = 9
As we can see, the ratio between Hours and Money is the same (9) for each row. This confirms that there is a constant ratio, indicating a proportional relationship between the two quantities.
Additionally, in a proportional relationship, if you double one quantity, the other quantity will also double. This can be observed in this example, where every time the Hours are multiplied by 2, the Money is also multiplied by 2.
Therefore, based on the calculated ratios and the doubling property, we can conclude that the data table represents a proportional relationship.