We want to determine the slope of the linear relationship given the table of values.
[tex]\[
\begin{array}{|c|c|c|c|c|c|}
\hline
x & -2 & -1 & 0 & 1 & 2 \\
\hline
y & -12 & -7 & -2 & 3 & 8 \\
\hline
\end{array}
\][/tex]
To find the slope [tex]\(m\)[/tex] of the linear relationship, we use the formula for the slope between any 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]
Let's pick the first two points from the table:
- Point A: [tex]\((-2, -12)\)[/tex]
- Point B: [tex]\((-1, -7)\)[/tex]
Now, let's calculate the difference in y-values and x-values between these two points.
[tex]\[
\Delta y = y_2 - y_1 = -7 - (-12)
\][/tex]
[tex]\[
\Delta y = -7 + 12 = 5
\][/tex]
[tex]\[
\Delta x = x_2 - x_1 = -1 - (-2)
\][/tex]
[tex]\[
\Delta x = -1 + 2 = 1
\][/tex]
Using these differences, we can now determine the slope:
[tex]\[
m = \frac{\Delta y}{\Delta x} = \frac{5}{1} = 5
\][/tex]
Therefore, the slope of the linear relationship is [tex]\(5\)[/tex], which matches one of the given answer choices. Thus, the correct answer is:
[tex]\(5\)[/tex]
