To determine whether the data set is linear or nonlinear, we should look at the rate of change between the "Months Passed" and the "Total Houses Built".
Let's calculate the rate of change between each pair of points for "Total Houses Built" relative to "Months Passed":
1. From month 0 to month 3:
- Increase in months = 3 - 0 = 3 months
- Increase in houses = 33 - 0 = 33 houses
- Rate of change = 33 houses / 3 months = 11 houses per month
2. From month 3 to month 4:
- Increase in months = 4 - 3 = 1 month
- Increase in houses = 46 - 33 = 13 houses
- Rate of change = 13 houses / 1 month = 13 houses per month
3. From month 4 to month 8:
- Increase in months = 8 - 4 = 4 months
- Increase in houses = 108 - 46 = 62 houses
- Rate of change = 62 houses / 4 months = 15.5 houses per month
The rate of change is not constant: it changes from 11 houses per month to 13 houses per month to 15.5 houses per month. This varying rate of change indicates that the data set is nonlinear.
Thus, the correct conclusion is:
**It is nonlinear because the increase in the “Total Houses Built” compared to the increase in the “Months Passed” does not show a constant rate of change.**
The function in the table below shows the relationship between the total number of houses built in an area and the number of months that passed.
A two column table with five rows. The first column, Months Passed, has the entries, 0, 3, 4, 8. The second column, Total Houses Built, has the entries 0, 33, 46, 108.
Which best describes the data set?
It is nonlinear because the “Total Houses Built” column does not increase at a constant additive rate.
It is nonlinear because the “Months Passed” column does not increase at a constant additive rate.
It is nonlinear because the increase in the “Total Houses Built” compared to the increase in the “Months Passed” does not show a constant rate of change.
It is linear because the increase in the “Total Houses Built” compared to the increase in the “Months Passed” shows a constant rate of change
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