Question

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. 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.

months passed	total houses built
3	33
4	46
8	108

Explanation:

Step1: Recall linear - function property

A linear function has a constant rate of change, which means $\frac{\Delta y}{\Delta x}$ (change in $y$ over change in $x$) is constant. Here, let $x$ be the "Months Passed" and $y$ be the "Total Houses Built".

Step2: Calculate rate of change between first two points

For the points $(0,0)$ and $(3,33)$: $\frac{\Delta y}{\Delta x}=\frac{33 - 0}{3-0}=\frac{33}{3}=11$.

Step3: Calculate rate of change between second and third points

For the points $(3,33)$ and $(4,46)$: $\frac{\Delta y}{\Delta x}=\frac{46 - 33}{4 - 3}=\frac{13}{1}=13$.

Step4: Analyze non - constancy

Since the rate of change $\frac{\Delta y}{\Delta x}$ is not constant (11 $
eq$ 13), the data set 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.

Answer:

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.