To determine whether the given dataset represents a linear or nonlinear relationship, we need to check if the rate of change (or slope) between the data points is constant. This is done by comparing the differences in 'Total Houses Built' relative to the differences in 'Months Passed' across each interval.
The data points provided are:
- (0 months, 0 houses)
- (3 months, 33 houses)
- (4 months, 46 houses)
- (8 months, 108 houses)
Let’s calculate the rate of change for each of the intervals between these data points.
1. From 0 to 3 months:
- Houses built: 33 - 0 = 33
- Months passed: 3 - 0 = 3
- Rate of change: 33 / 3 = 11 houses per month
2. From 3 to 4 months:
- Houses built: 46 - 33 = 13
- Months passed: 4 - 3 = 1
- Rate of change: 13 / 1 = 13 houses per month
3. From 4 to 8 months:
- Houses built: 108 - 46 = 62
- Months passed: 8 - 4 = 4
- Rate of change: 62 / 4 = 15.5 houses per month
Now, let’s examine the calculated rates of changes:
- From 0 to 3 months: 11 houses per month
- From 3 to 4 months: 13 houses per month
- From 4 to 8 months: 15.5 houses per month
We observe that the rate of change is not constant; it varies from one interval to another.
Therefore, we conclude:
The relationship 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.
