To determine the slope of a linear function given a table of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] values, we can use the formula for the slope (m) between two points, [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], which is:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Let’s choose the first two points from the provided table to calculate the slope:
- When [tex]\(x = -2\)[/tex], [tex]\(y = 8\)[/tex].
- When [tex]\(x = -1\)[/tex], [tex]\(y = 2\)[/tex].
Using these points:
- [tex]\((x_1, y_1) = (-2, 8)\)[/tex]
- [tex]\((x_2, y_2) = (-1, 2)\)[/tex]
Now, apply the slope formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 8}{-1 - (-2)} = \frac{2 - 8}{-1 + 2} = \frac{-6}{1} = -6 \][/tex]
Thus, the slope of the function is [tex]\(-6\)[/tex].
The correct choice from the given options is [tex]\(-6\)[/tex].
