Question

Which best describes the data set?

Answer 1

Answer: It is nonlinear because the increase in the "Total house built" compared to the "Months Passed" does not show a constant rate of change.

Explanation:

We say function to be linear if the rate of change in dependent variable (y) with respect to independent variable (x) is constant.

Rate of change =
`\frac{\text{Change in dependent variable}}{\text{Change in independent variable}}`

According to the question ,

Independent variable = Number of months

Dependent variable = Total house built

Now rate of change of "Total house built" for month 0 to 3:-

`(33-0)/(3-0)=(33)/(3)=11` (1)

Rate of change of "Total house built"fro month 3 to 4:-

`(46-33)/(4-3)=(13)/(1)=13` (2)

From (1) and (2), it is clear that the rate of change is not constant

(∵ 11≠ 13 ).

Hence, the correct answer is : It is nonlinear because the increase in the "Total house built" compared to the "Months Passed" does not show a constant rate of change.

Answer 2

The answer is C

Explanation:

It is nonlinear but you have to look at it compared to the months passed. In three months the total houses built are 33 this would mean each month they build 11 houses but in the fourth month they have built 46 houses because 46-11 dosnt equal 33 it is nonlinear.