To determine the slope of the linear function given by the table of values, we follow these steps:
1. Identify two points from the table:
We can select any two points to calculate the slope. For simplicity, let's choose the first two points:
- Point 1: [tex]\((-2, 8)\)[/tex]
- Point 2: [tex]\((-1, 2)\)[/tex]
2. Calculate the change in [tex]\(y\)[/tex] values ([tex]\(\Delta y\)[/tex]):
[tex]\[
\Delta y = y_2 - y_1 = 2 - 8 = -6
\][/tex]
3. Calculate the change in [tex]\(x\)[/tex] values ([tex]\(\Delta x\)[/tex]):
[tex]\[
\Delta x = x_2 - x_1 = -1 - (-2) = -1 + 2 = 1
\][/tex]
4. Calculate the slope ([tex]\(m\)[/tex]):
The slope of a linear function is given by the ratio of the change in [tex]\(y\)[/tex] to the change in [tex]\(x\)[/tex]:
[tex]\[
m = \frac{\Delta y}{\Delta x} = \frac{-6}{1} = -6
\][/tex]
Thus, the slope of the function is [tex]\(-6\)[/tex].
Given the options:
- [tex]\(-6\)[/tex]
- [tex]\(-4\)[/tex]
- 4
- 6
The correct answer is [tex]\(-6\)[/tex].
So the correct choice to mark is:
[tex]\[ \boxed{-6} \][/tex]
