To find a good approximation for the value of the function [tex]\( f(x) \)[/tex] when [tex]\( x = 18 \)[/tex] using the given line of best fit [tex]\( f(x) = -0.86x + 13.5 \)[/tex], we proceed as follows:
1. Start with the given equation of the line of best fit:
[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. Perform the multiplication:
[tex]\[
-0.86 \cdot 18 = -15.48
\][/tex]
4. Then add the constant term:
[tex]\[
f(18) = -15.48 + 13.5
\][/tex]
5. Calculate the sum:
[tex]\[
f(18) = -1.98
\][/tex]
So, the value of [tex]\( f(x) \)[/tex] when [tex]\( x = 18 \)[/tex] is [tex]\( -1.98 \)[/tex].
Therefore, a good approximation for the value of the function [tex]\( f(x) \)[/tex] when [tex]\( x = 18 \)[/tex] is [tex]\[ \boxed{-1.98} \][/tex].
