Question

During a housing boom the price of houses increased over an 18 month period.A house that cost 240000 at the start of the period had a sale value of 276000 atthe end of the period. What was the average rate of change in the price per month?

Answer 1

`m=2,000\text{ / month}`

Step-by-step explanation: We have to find the average rate of change in price per month, this problem can be modeled by using the standard equation of the line:

`y(x)=mx+b`

Where y(x) is the house cost as a function of the month and the "m" is defined as follows:

`m=(\Delta y)/(\Delta x)\Rightarrow(1)`

In other words, m is the change in house cost over the change in the months:

`m=(\Delta y)/(\Delta x)=(276000-240000)/(18-0)=(36000)/(18)=2000`

Conclusion: Therefore the average change in the cost per month is as follows;

`m=2000\text{ /month}`

The standard equation that can model it is as follows:

`\begin{gathered} y(x)=2000x+0 \\ b=0 \\ y(x)=2000x \end{gathered}`