Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

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]