The table shows how much a carpenter charges for work. Is the relationship shown by the data in the table linear? Explain your answer. 1 25 2 40 3 60 4 80
To determine if the relationship shown by the data in the table is linear, we can examine the change in the charges as the number of work increases.
In this table, when the number of work doubles (e.g., from 1 to 2), the charge increases by $15 (from $25 to $40). Similarly, when the number of work doubles again (e.g., from 2 to 4), the charge increases by $20 (from $40 to $80).
This indicates that the rate of increase in the charge is not constant. In a linear relationship, the rate of change would remain consistent throughout. However, here, we see that the charge increases at a faster rate as the number of work increases.
Therefore, the relationship shown by the data in the table is not linear.