To determine the slope of the linear function represented by the given table, follow these steps:
1. Select any two points from the table. Let's choose the points [tex]\((-2, 8)\)[/tex] and [tex]\((-1, 2)\)[/tex].
2. Use the slope formula:
[tex]\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
where [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are two points on the line.
3. Plug in the coordinates of the selected points into the formula. For the points [tex]\((-2, 8)\)[/tex] and [tex]\((-1, 2)\)[/tex]:
[tex]\[
x_1 = -2, \quad y_1 = 8, \quad x_2 = -1, \quad y_2 = 2
\][/tex]
4. Substitute these values into the slope formula:
[tex]\[
\text{slope} = \frac{2 - 8}{-1 - (-2)} = \frac{-6}{1} = -6
\][/tex]
5. Therefore, the slope of the function is [tex]\(-6\)[/tex].
So the correct option is:
[tex]\[
-6
\][/tex]
