The following table represents the total cost, in dollars (y) to join a gym for ex number of months. The cost includes one time joining fee of $10. Does the data in the table represent a proportional relationship or non-proportion relationship? How do you know?
X 1, 2, 3, 4, 5
Y 25,40,55,70,85
AAAaannndd the bot gets it wrong yet again!
non-proportional
To determine whether the data in the table represents a proportional or non-proportional relationship, we can analyze the rate of change between the two variables.
In a proportional relationship, the rate of change between the two variables is constant. This means that for every increase in x, there is a consistent increase in y.
Let's calculate the rate of change for the given data points by taking the difference between consecutive y-values divided by the difference between consecutive x-values:
For x = 1 to x = 2:
Rate of change = (40 - 25) / (2 - 1) = 15
For x = 2 to x = 3:
Rate of change = (55 - 40) / (3 - 2) = 15
For x = 3 to x = 4:
Rate of change = (70 - 55) / (4 - 3) = 15
For x = 4 to x = 5:
Rate of change = (85 - 70) / (5 - 4) = 15
As we can see, the rate of change between the x-values and the y-values is constant at 15. Therefore, the data in the table represents a proportional relationship.
To determine if the data in the table represents a proportional or non-proportional relationship, we need to check if there is a constant ratio between the values of x and y.
In a proportional relationship, the ratio between the values of x and y will always remain the same. This means that if we divide any y-value by its corresponding x-value, we should get the same result.
Let's calculate the ratios for the given data:
Ratio for x=2: y=40 / x=2 = 20
Ratio for x=3: y=55 / x=3 = 18.33
Ratio for x=4: y=70 / x=4 = 17.5
Ratio for x=5: y=85 / x=5 = 17
From the above ratios, we can see that the values are not the same. Therefore, the data in the table does not represent a proportional relationship.
Another way to see this is by comparing the differences between the y-values. If the differences are always the same, then it's a proportional relationship. Let's calculate the differences:
Difference between y=40 and y=25: 40 - 25 = 15
Difference between y=55 and y=40: 55 - 40 = 15
Difference between y=70 and y=55: 70 - 55 = 15
Difference between y=85 and y=70: 85 - 70 = 15
Since the differences between the y-values are not the same, we can conclude that the data does not represent a proportional relationship.
Therefore, the data in the table represents a non-proportional relationship.