Using the equation for the line of best fit, [tex]\( f(x) = -0.86x + 13.5 \)[/tex], approximate the value of the function [tex]\( f(x) \)[/tex] when [tex]\( x = 18 \)[/tex].

Given the set of points in the table:

[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $f(x)$ \\
\hline
2 & 12 \\
\hline
3 & 10 \\
\hline
5 & 10 \\
\hline
6 & 8 \\
\hline
7 & 9 \\
\hline
8 & 5 \\
\hline
9 & 6 \\
\hline
\end{tabular}
\][/tex]

A. [tex]\(\leq 6\)[/tex]
B. 42
C. 3
D. 12



Answer :

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].