Question

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

Answer 1

are you sure

Answer 2

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.

Answer 3

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.