A house is listed for sale at $250,000, but the listing does not include the square footage of the house. Based on the comps, the line of best fit is [tex]$ y = 0.07x + 50.5 $[/tex]. If the price is fair, what size (in square feet) should the house be?

A. [tex]$ 9240 \, ft^2 $[/tex]
B. [tex]$ 28.5 \, ft^2 $[/tex]
C. [tex]$ 17,000 \, ft^2 $[/tex]
D. [tex]$ 2850 \, ft^2 $[/tex]

To find the size of the house in square feet that corresponds to the fair listing price of $250,000, we can use the given linear equation of the best fit line, which is:

[tex]y = 0.07x + 50.5[/tex]

where:

x is the size of the house (in square feet).
y is the sale price of the house (in thousands of dollars).

First, convert the sale price into thousands of dollars:

[tex]y =\dfrac{250000}{1000}=250[/tex]

Next, substitute y = 250 into the given linear equation and solve for x:

[tex]250=0.07x+50.5 \\\\\\250-50.5=0.07x+50.5-50.5 \\\\\\199.5=0.07x\\\\\\\dfrac{199.5}{0.07}=\dfrac{0.07x}{0.07}\\\\\\x=2850[/tex]

Therefore, the house should be approximately 2,850 square feet to have a fair price of $250,000.