Write a linear model for the price of a home, P, as a function of the yeart. Let t=0 correspond to 1980.

Question

In 1980 the average price of a Home was $97000. By 1986 the average price of a home was $109,000. Write a linear model for the price of a home, P, as a function of the year, t. Let t=0 correspond to 1980.

Answer 1

Note that P is a linear function of t.  That is, P(t) = mt + b, where

     m = the slope (the change per year)

     b = the P-intercept (that is, the value of P when t=0)

 

At t=0 (that is, in 1980), P = $97000.  So, P(0) = $97000 means b=$97000.

The function looks like:      P(t) = mt + $97000

     What is m (that is, the yearly change)?

 

        The known points are:   (0,$97000) and (6,$109000)

           m, the slope, is ($109000-$97000)/(6 years - 0 years)

                                       ($12000)/(6 years)

                                          $2000 per year

 

The function is:      P(t) = $2000m + $97000

 

Check (always good to do):

   Is (0.$97000) a point on the line?

           Does   $97000 = $2000(0) + $97000   ?

                     $97000 = $97000   ?yes

   Is (6,$109000) a point on the line?

           Does    $109000 = $2000(6) + $97000   ?

                      $109000 = $12000 + $97000   ?

                     $109000 = $109000   ?yes