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 -
1.
2.
3.
4.
Money -
9.
18.
27.
36.

Answer 1

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.

Answer 2

can you make it step by step

Answer 3

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.