Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

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]
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.