To determine the slope of the function represented by the given table of values, we follow a detailed, step-by-step solution.
1. Identify and write down the given values:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-2 & 10 \\
\hline
0 & 4 \\
\hline
4 & -8 \\
\hline
6 & -14 \\
\hline
9 & -23 \\
\hline
\end{array}
\][/tex]
2. Determine the change in [tex]\( x \)[/tex] values (Δx):
The first [tex]\( x \)[/tex] value is [tex]\( -2 \)[/tex] and the last [tex]\( x \)[/tex] value is [tex]\( 9 \)[/tex].
[tex]\[
\Delta x = 9 - (-2) = 9 + 2 = 11
\][/tex]
3. Determine the change in [tex]\( y \)[/tex] values (Δy):
The first [tex]\( y \)[/tex] value is [tex]\( 10 \)[/tex] and the last [tex]\( y \)[/tex] value is [tex]\( -23 \)[/tex].
[tex]\[
\Delta y = -23 - 10 = -33
\][/tex]
4. Calculate the slope (m):
The slope is defined as the change in [tex]\( y \)[/tex] divided by the change in [tex]\( x \)[/tex]:
[tex]\[
m = \frac{\Delta y}{\Delta x} = \frac{-33}{11} = -3
\][/tex]
The slope of the function is therefore [tex]\(-3\)[/tex]. Thus, the correct answer is:
C. [tex]\(-3\)[/tex]
