To determine the slope of the function, we need to use the slope formula given two points on the line. The slope formula is:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here, we will use the first two points from the table: [tex]\((-2, 10)\)[/tex] and [tex]\( (0, 4) \)[/tex].
Let's denote:
- The first point [tex]\((-2, 10)\)[/tex] as [tex]\((x_1, y_1)\)[/tex]
- The second point [tex]\( (0, 4) \)[/tex] as [tex]\((x_2, y_2)\)[/tex]
Substituting these points into the slope formula, we get:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
[tex]\[ m = \frac{4 - 10}{0 - (-2)} \][/tex]
[tex]\[ m = \frac{4 - 10}{0 + 2} \][/tex]
[tex]\[ m = \frac{-6}{2} \][/tex]
[tex]\[ m = -3 \][/tex]
So, the slope of the function is [tex]\(-3\)[/tex]. Therefore, the correct answer is:
B. -3
