To find the fair price for the house, we need to use the line of best fit equation provided, which is [tex]\( y = 0.074x + 50.48 \)[/tex]. Here, [tex]\( y \)[/tex] represents the price of the house in thousands of dollars, and [tex]\( x \)[/tex] represents the area of the house in square feet.
Given the house size is [tex]\( 1700 \ \text{ft}^2 \)[/tex], we substitute [tex]\( x = 1700 \)[/tex] into the equation to find [tex]\( y \)[/tex].
1. Start with the given line of best fit equation:
[tex]\[
y = 0.074x + 50.48
\][/tex]
2. Substitute [tex]\( x = 1700 \)[/tex] into the equation:
[tex]\[
y = 0.074 \times 1700 + 50.48
\][/tex]
3. Calculate [tex]\( 0.074 \times 1700 \)[/tex]:
[tex]\[
0.074 \times 1700 = 125.8
\][/tex]
4. Add the intercept [tex]\( 50.48 \)[/tex] to the product:
[tex]\[
125.8 + 50.48 = 176.28
\][/tex]
So, the fair price for the house, according to the line of best fit, is [tex]\(\$176.28\)[/tex] thousand dollars, which equals \[tex]$176,280 when converted to standard dollar format. Among the given choices, the correct answer is:
D. \(\$[/tex]176.28\)
