Solve. Please

Question

In 2006, the median of an existing home in some country was approximately $224,000. In 2001 the median of an existing home was $151,400. Let y be the median price of any existing home in year x.  Where x=0  represents 2001.  (Show all Work)

A) Write an linear equation that models the median existing home price in terms of year x. (hint the line must pass through the points (0,151400) and (5,224000).) (Type the answer in slope-intercept form)

B) Use the linear equation to predict the median existing home price for the year 2010.

C)Interpret the slope of the equation found in part a. Choose the best answer 

     a) Every year, the median of a home increases by $14,520

     b) Every year, the median of a home decreases by $151,400.

     c) Every year, the median of a home decreases by $14,520

     d) Every year, the median of a home increase by $151,400. 

Answer 1

y = median price of home in year x

 

For simplicity's sake, x = 0 (for 2001), x=1 (for 2002), .... x=5 (for 2006)

 

Slope of line, therefore, = [($224,000 - $151,400)/5 years] = $14,520 per year

 

A.  Therefore y = ($14,520/year)x + b = ($14,520/year)x + $151,400

 

B.  For the year 2010

 

y = ($14,520/year)(9 years) + $151,400 = $282,080

 

C.  The answer is a).  Every year the median home price increases by $14,520. That is the physical meaning of the slope of the line.

Answer 2

Points  (0,151400) and (5,224000)

 

Using the Point-Slope Form of the equation of a straight line to solve for m 

 

(y1 - y) = m(x1 - x)

 

(224000 - 151400) = m(5 - 0)

 

 m =72600 / 5 = 14520

 

Using the equation of a straight line  y = m x + c  solve for c

 

151400 = 14520 x  0 + c

 

c = 151400

 

Linear equation that models the median y = 14520 x + 151400

 

The median existing home price for the year 2010.

 

y = 14520 x + 151400 where x =9

 

y = 14520 x 9+ 151400

 

y =130680 + 151400 = 282080

 

(a)  Every year, the median of a home increases by $14,520