the table shows how much a carpenter charges for work is the relationship shown by data in the table linear?
1 25
2 40
3 60
4 80
To determine if the relationship shown by the data in the table is linear, we need to check if there is a constant rate of change between the values in the first column and the corresponding values in the second column.
The rate of change is calculated by finding the difference between consecutive values in the second column and dividing it by the difference between the corresponding values in the first column.
1st difference in second column: 40 - 25 = 15
1st difference in first column: 2 - 1 = 1
Rate of change: (15) / (1) = 15
2nd difference in second column: 60 - 40 = 20
2nd difference in first column: 3 - 2 = 1
Rate of change: (20) / (1) = 20
3rd difference in second column: 80 - 60 = 20
3rd difference in first column: 4 - 3 = 1
Rate of change: (20) / (1) = 20
Since the rate of change is consistent and equal to 20, we can conclude that the relationship shown by the data in the table is linear.
are you sure
Apologies for the previous confusion. The rate of change between consecutive values in the second column is not constant. Here are the calculations to determine if the relationship shown by the data in the table is linear:
1st difference in second column: 40 - 25 = 15
1st difference in first column: 2 - 1 = 1
Rate of change: (15) / (1) = 15
2nd difference in second column: 60 - 40 = 20
2nd difference in first column: 3 - 2 = 1
Rate of change: (20) / (1) = 20
3rd difference in second column: 80 - 60 = 20
3rd difference in first column: 4 - 3 = 1
Rate of change: (20) / (1) = 20
Since the rate of change is inconsistent (15, 20, 20), we can conclude that the relationship shown by the data in the table is not linear.
To determine if the relationship shown by the data in the table is linear, we can examine if there is a constant rate of change between the values. A linear relationship means that for every increase in the independent variable (in this case, the input values), there is a consistent increase or decrease in the dependent variable (the output values).
Let's calculate the rate of change between the input values:
From 1 to 2:
The change in the input values is 2 - 1 = 1.
The change in the output values is 40 - 25 = 15.
Rate of change = change in output / change in input = 15 / 1 = 15.
From 2 to 3:
The change in the input values is 3 - 2 = 1.
The change in the output values is 60 - 40 = 20.
Rate of change = change in output / change in input = 20 / 1 = 20.
From 3 to 4:
The change in the input values is 4 - 3 = 1.
The change in the output values is 80 - 60 = 20.
Rate of change = change in output / change in input = 20 / 1 = 20.
Since the rate of change between all the consecutive values is consistent (15, 20, 20), we can conclude that the relationship shown by the data in the table is linear.