To find the slope of a linear relationship, you use two points from the table of values and apply the slope formula. The slope [tex]\( m \)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is calculated as follows:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
We can choose any two points from the table. Let's use the points [tex]\((-4, 11)\)[/tex] and [tex]\((2, -1)\)[/tex].
1. Identify the coordinates of the points:
- First point: [tex]\((x_1, y_1) = (-4, 11)\)[/tex]
- Second point: [tex]\((x_2, y_2) = (2, -1)\)[/tex]
2. Substitute the coordinates into the slope formula:
[tex]\[
m = \frac{-1 - 11}{2 - (-4)}
\][/tex]
3. Simplify the numerator and the denominator:
[tex]\[
m = \frac{-12}{2 + 4}
\][/tex]
4. Simplify further:
[tex]\[
m = \frac{-12}{6}
\][/tex]
5. Divide to find the slope:
[tex]\[
m = -2
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{-2}
\][/tex]
So, the slope of the linear relationship shown in the table of values is [tex]\(\boxed{-2}\)[/tex]. The correct answer is B.
