Questions: A line of best fit is f(x)=-0.86 x+13.5 for the set of points in the table.
x f(x)
2 12
3 10
5 10
6 8
7 9
8 5
9 6
Using the equation for the line of best fit, what is a good approximation for the value of the function, f(x), when x= 18 ?
-5
-2
3
12
Transcript text: 47:02
A line of best fit is $f(x)=-0.86 x+13.5$ for the set of points in the table.
\begin{tabular}{|c|c|}
\hline $\boldsymbol{x}$ & $\boldsymbol{f} \boldsymbol{x} \boldsymbol{)}$ \\
\hline 2 & 12 \\
\hline 3 & 10 \\
\hline 5 & 10 \\
\hline 6 & 8 \\
\hline 7 & 9 \\
\hline 8 & 5 \\
\hline 9 & 6 \\
\hline
\end{tabular}
Using the equation for the line of best fit, what is a good approximation for the value of the function, $f(x)$, when $x=$ 18 ?
$-5$
$-2$
3
12
Solution
Solution Steps
Step 1: Determine the Line of Best Fit
The line of best fit is given by the equation:
\[
f(x) = -0.86x + 13.5
\]
Step 2: Substitute the Value of \( x \)
We need to find the value of the function \( f(x) \) when \( x = 18 \). Substituting \( x \) into the equation:
\[
f(18) = -0.86(18) + 13.5
\]
Step 3: Calculate the Result
Calculating the expression:
\[
f(18) = -15.48 + 13.5 = -1.98
\]
Final Answer
The value of the function \( f(x) \) when \( x = 18 \) is approximately