To determine the slope of the linear relationship given in the table of values, we can use the formula for the slope between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Here are the given points from the table:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-4 & 11 \\
\hline
2 & -1 \\
\hline
5 & -7 \\
\hline
\end{array}
\][/tex]
First, we calculate the slope using the points [tex]\((-4, 11)\)[/tex] and [tex]\((2, -1)\)[/tex].
[tex]\[
m = \frac{-1 - 11}{2 - (-4)} = \frac{-1 - 11}{2 + 4} = \frac{-12}{6} = -2
\][/tex]
Next, we should confirm that the same slope applies between the points [tex]\((2, -1)\)[/tex] and [tex]\((5, -7)\)[/tex].
[tex]\[
m = \frac{-7 - (-1)}{5 - 2} = \frac{-7 + 1}{5 - 2} = \frac{-6}{3} = -2
\][/tex]
Since the slope between both pairs of points is the same [tex]\(-2\)[/tex], we can conclude that this is the slope of the linear relationship.
Thus, the correct answer is:
B. -2
