The table shows how much a carpenter charges for work. Is the relationship shown by the data in the table linear? Explain your answer.
A two column table is shown. The first column is titled 'Hours Worked' and contains the values 1, 2, 3, and 4 from top to bottom. The second column is titled 'Amount Charged in Dollars' and contains the values 25, 40, 60, and 80 from top to bottom.
To determine if the relationship shown by the data in the table is linear, we need to analyze the rate of change between the variables. In a linear relationship, the rate of change between the variables remains constant.
Let's calculate the rate of change between each pair of consecutive values in the 'Hours Worked' and 'Amount Charged in Dollars' columns:
- The rate of change between 1 and 2 hours is $40 - $25 = $15.
- The rate of change between 2 and 3 hours is $60 - $40 = $20.
- The rate of change between 3 and 4 hours is $80 - $60 = $20.
As we can see, the rate of change is not constant. Between 1 and 2 hours, the amount charged increases by $15, but between 2 and 3 hours, the increase is $20. This indicates that the relationship between 'Hours Worked' and 'Amount Charged in Dollars' is not linear.
Therefore, 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 need to check if there is a constant rate of change.
Let's calculate the differences between consecutive values in the 'Amount Charged in Dollars' column:
- The difference between 40 and 25 is 15.
- The difference between 60 and 40 is 20.
- The difference between 80 and 60 is 20.
Since the differences are not constant, this indicates that the relationship is not linear. In a linear relationship, the differences between consecutive values should be the same. Therefore, the data in the table does not exhibit a linear relationship.