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What is the slope of the function represented by the table of values below?

\begin{tabular}{|c|c|}
\hline [tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline -2 & 10 \\
\hline 0 & 4 \\
\hline 4 & -8 \\
\hline 6 & -14 \\
\hline 9 & -23 \\
\hline
\end{tabular}

A. -6
B. -2
C. -3
D. -4

Sagot :

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]