Sure, let's go through the calculation step-by-step to find the slope of the linear function represented by the table.
The table provided is:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
-2 & 8 \\
\hline
-1 & 2 \\
\hline
0 & -4 \\
\hline
1 & -10 \\
\hline
2 & -16 \\
\hline
\end{tabular}
\][/tex]
### Step-by-Step Calculation:
1. Identify Two Points: We will use the first two points from the table to calculate the slope. Let's choose ([tex]\(x_1, y_1\)[/tex]) = (-2, 8) and ([tex]\(x_2, y_2\)[/tex]) = (-1, 2).
2. Calculate the Differences:
[tex]\[
\Delta y = y_2 - y_1 = 2 - 8 = -6
\][/tex]
[tex]\[
\Delta x = x_2 - x_1 = -1 - (-2) = -1 + 2 = 1
\][/tex]
3. Calculate the Slope [tex]\(m\)[/tex]:
The slope [tex]\(m\)[/tex] is given by the formula:
[tex]\[
m = \frac{\Delta y}{\Delta x} = \frac{-6}{1} = -6
\][/tex]
The slope of the linear function represented by the table is [tex]\(-6\)[/tex]. Therefore, the correct answer is:
[tex]\[
\boxed{-6}
\][/tex]
