The table shows how much a carpenter charges for work. Is the relationship shown by the data in the table linear or nonlinear?
1 25
2 40
3 60
4 80
I think it is linear, but can you check my work?
nonlinear.
why?
non-linear , because the increase between steps is not equal:
25+15 = 40
40+15 = 55
55+15 = 70
70+15 = 85
The data above is required for linearity.
t
To determine whether the relationship shown by the data in the table is linear or nonlinear, we can examine if there is a constant difference between the terms. Let's calculate the differences between consecutive terms:
The difference between 25 and 40 is 40 - 25 = 15.
The difference between 40 and 60 is 60 - 40 = 20.
The difference between 60 and 80 is 80 - 60 = 20.
As we can see, the differences are not constant. The difference between the terms varies, indicating a nonlinear relationship. Therefore, the relationship shown by the data in the table is nonlinear, not linear.
To determine whether the relationship shown by the data in the table is linear or nonlinear, you can follow these steps:
1. Look for a constant rate of change between the values in the table. In a linear relationship, the rate of change will remain consistent.
2. Calculate the differences between consecutive values in the table. For example, between 1 and 2, the difference is 40 - 25 = 15. Then between 2 and 3, the difference is 60 - 40 = 20. Lastly, between 3 and 4, the difference is 80 - 60 = 20.
3. Compare the differences. If the differences between consecutive values are the same, then the relationship is linear. However, if the differences vary, the relationship is nonlinear.
In this case, the differences are not the same. Between 1 and 2, the difference is 15, and between 2 and 3, the difference is 20. Therefore, the differences indicate a nonlinear relationship between the values.
Therefore, based on the information provided, the relationship shown by the data in the table is nonlinear, not linear.