The table shows how much a carpenter charges for work. Is the relationship shown by the data in the table linear? Explain your answer.
Hours Worked
1
2
3
4
Amount Charged (S)
25
40
60
80
To determine whether the relationship shown by the data in the table is linear, we can examine the pattern of the given values.
Looking at the table, we can observe that as the number of hours worked increases, the amount charged also increases. However, the rate at which the amount charged increases is not constant.
For example, between 1 and 2 hours worked, the amount charged increases by $15 (from $25 to $40). Then, between 2 and 3 hours worked, the amount charged increases by $20 (from $40 to $60). Lastly, between 3 and 4 hours worked, the amount charged increases by $20 again (from $60 to $80).
Since the increase in the amount charged is not consistent, the relationship between the hours worked and the amount charged is not linear.