To determine the slope of the linear function represented by the given table, we need to use the values of two points from the table. The formula to calculate the slope [tex]\( m \)[/tex] of a line passing through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Let's choose the first two points from the table:
- The first point is [tex]\((x_1, y_1) = (-2, 8)\)[/tex]
- The second point is [tex]\((x_2, y_2) = (-1, 2)\)[/tex]
Now plug these values into the slope formula:
[tex]\[ m = \frac{2 - 8}{-1 - (-2)} \][/tex]
First, simplify the numerator and the denominator separately:
- Numerator: [tex]\( 2 - 8 = -6 \)[/tex]
- Denominator: [tex]\( -1 - (-2) = -1 + 2 = 1 \)[/tex]
So the slope calculation becomes:
[tex]\[ m = \frac{-6}{1} \][/tex]
Therefore, the slope [tex]\( m \)[/tex] is:
[tex]\[ m = -6 \][/tex]
The correct answer is:
[tex]\[ -6 \][/tex]
