To determine the fair price for a house that is [tex]\(1700 \, \text{ft}^2\)[/tex] given the line of best fit [tex]\(y = 0.074x + 50.48\)[/tex], we can follow these steps:
1. Identify the Given Values:
- House size, [tex]\(x = 1700 \, \text{ft}^2\)[/tex]
- Slope of the line, [tex]\(m = 0.074\)[/tex]
- Y-intercept, [tex]\(b = 50.48\)[/tex]
2. Write the Equation:
The equation for the line of best fit is:
[tex]\[
y = 0.074x + 50.48
\][/tex]
3. Substitute the House Size into the Equation:
Plug in [tex]\(x = 1700\)[/tex] into the equation to calculate [tex]\(y\)[/tex]:
[tex]\[
y = 0.074 \cdot 1700 + 50.48
\][/tex]
4. Calculate the Price:
Perform the calculation step by step:
[tex]\[
0.074 \cdot 1700 = 125.8
\][/tex]
[tex]\[
125.8 + 50.48 = 176.28
\][/tex]
5. Result:
The price, [tex]\(y\)[/tex], for a house that is [tex]\(1700 \, \text{ft}^2\)[/tex] is [tex]\(176.28\)[/tex].
6. Compare with Given Options:
Now compare the calculated price with the given options:
- Option A: [tex]$\$[/tex]150,000[tex]$
- Option B: $[/tex]\[tex]$176,000$[/tex]
- Option C: [tex]$\$[/tex]150.00[tex]$
- Option D: $[/tex]\[tex]$176.28$[/tex]
The calculated price [tex]\(176.28\)[/tex] matches exactly with Option D.
Therefore, the fair price for the house is [tex]\( \$176.28 \)[/tex].
