To find the value of the function [tex]\(f(x)\)[/tex] when [tex]\(x = 18\)[/tex] using the equation of the line of best fit given by [tex]\(f(x) = -0.86x + 13.5\)[/tex], follow these steps:
1. Start with the given equation: [tex]\(f(x) = -0.86x + 13.5\)[/tex].
2. Substitute [tex]\(x = 18\)[/tex] into the equation.
[tex]\[
f(18) = -0.86 \cdot 18 + 13.5
\][/tex]
3. Calculate the product [tex]\(-0.86 \cdot 18\)[/tex].
4. After obtaining that product, add the constant term [tex]\(13.5\)[/tex].
Combining these steps, you get:
[tex]\[
f(18) = -0.86 \cdot 18 + 13.5 = -1.98
\][/tex]
Therefore, the good approximation for the value of the function when [tex]\(x = 18\)[/tex] is [tex]\(-2\)[/tex].
The choice closest to [tex]\(-1.98\)[/tex] is [tex]\(-2\)[/tex]. Hence, the correct approximation is:
[tex]\[
\boxed{-2}
\][/tex]
