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 money = 9
hours = 2 money = 18
hours = 3 money = 27
hours = 4 money = 36
To show that the table represents a proportional relationship, we need to verify if the ratio between the hours and money stays constant.
Let's calculate the ratio for each pair of values:
For the first pair:
hours = 1, money = 9
Ratio = money/hours = 9/1 = 9
For the second pair:
hours = 2, money = 18
Ratio = money/hours = 18/2 = 9
For the third pair:
hours = 3, money = 27
Ratio = money/hours = 27/3 = 9
For the fourth pair:
hours = 4, money = 36
Ratio = money/hours = 36/4 = 9
In each calculation, the ratio between the money and hours is 9. Since the ratio is constant for all the pairs of values, we can conclude that the table represents a proportional relationship.
It takes Julian 1 over 2 hour to walk 2 miles. He decides to start working in his spare time, but because he wants to make sure he has enough time to go a desired distance he created the data table. At which ratio does the constant of proportionality appear?
hours = 1 over 4 / miles walked = 1
hours = 1 over 2 / miles walked =2
hours = 3 over 4 / miles walked = 3
hours = 1 / miles walked = 4
To determine the ratio at which the constant of proportionality appears, we need to calculate the ratio between the hours and miles walked for each pair of values.
For the first pair:
hours = 1/4, miles walked = 1
Ratio = miles walked / hours = 1 / (1/4) = 4/1 = 4
For the second pair:
hours = 1/2, miles walked = 2
Ratio = miles walked / hours = 2 / (1/2) = 4/1 = 4
For the third pair:
hours = 3/4, miles walked = 3
Ratio = miles walked / hours = 3 / (3/4) = 4/1 = 4
For the fourth pair:
hours = 1, miles walked = 4
Ratio = miles walked / hours = 4 / (1/1) = 4/1 = 4
In each calculation, the ratio between the miles walked and hours is 4. Therefore, the constant of proportionality appears at a ratio of 4.
oh here are the options
A ( 1 over 4, 1)
B (4,1)
C (1,4)
D (1, 1 over 4)
The correct answer is C) (1, 4). In each calculation, the ratio between the hours and miles walked is 4. So the constant of proportionality appears at a ratio of 1:4.
To determine if the data table represents a proportional relationship, we need to check if there is a constant ratio between the values of hours and money. Here's how we can show our work:
1. Calculate the ratio between the hours and money for each row:
- For the first row: 1 hour / 9 money = 1/9 = 0.1111...
- For the second row: 2 hours / 18 money = 2/18 = 0.1111...
- For the third row: 3 hours / 27 money = 3/27 = 0.1111...
- For the fourth row: 4 hours / 36 money = 4/36 = 0.1111...
2. As we can see, the ratio between hours and money remains constant in each row, and it's approximately 0.1111....
Therefore, since there is a constant ratio between the hours and money values in the data table, we can conclude that the table represents a proportional relationship.