Answer :
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]
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]
