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 need to check if there is a constant rate of change between the independent variable (1, 2, 3, 4) and the dependent variable (25, 40, 60, 80).
Let's calculate the rate of change between each pair of values:
From 1 to 2:
Change in x = 2 - 1 = 1
Change in y = 40 - 25 = 15
From 2 to 3:
Change in x = 3 - 2 = 1
Change in y = 60 - 40 = 20
From 3 to 4:
Change in x = 4 - 3 = 1
Change in y = 80 - 60 = 20
As we can see, the rate of change in the y-values is not constant. The change in y between the first two points is 15, but the change in y between the second two points is 20. Therefore, the relationship shown by the data in the table is not linear.