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.
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.
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