To find the slope of the line that contains the points [tex]\((-1, 8)\)[/tex] and [tex]\( (5, -4) \)[/tex], we use the slope formula.
The slope [tex]\(m\)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by the formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Given points are:
[tex]\[
(x_1, y_1) = (-1, 8)
\][/tex]
[tex]\[
(x_2, y_2) = (5, -4)
\][/tex]
Now, substitute these values into the formula:
[tex]\[
m = \frac{-4 - 8}{5 - (-1)}
\][/tex]
First, simplify the numerator:
[tex]\[
-4 - 8 = -12
\][/tex]
Then, simplify the denominator:
[tex]\[
5 - (-1) = 5 + 1 = 6
\][/tex]
So, the slope [tex]\(m\)[/tex] becomes:
[tex]\[
m = \frac{-12}{6} = -2
\][/tex]
The answer is [tex]\( \boxed{-2} \)[/tex], which corresponds to option A.
