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

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
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Solution

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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

\[ \boxed{-1.98} \]

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