To determine the slope of the line containing the points [tex]\( J(1, -4) \)[/tex] and [tex]\( K(-2, 8) \)[/tex], we will use the slope formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
where [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are the coordinates of the two points. Here, let:
- [tex]\( J(1, -4) \)[/tex] correspond to [tex]\((x_1, y_1) = (1, -4) \)[/tex]
- [tex]\( K(-2, 8) \)[/tex] correspond to [tex]\((x_2, y_2) = (-2, 8) \)[/tex]
Plugging the values into the slope formula, we get:
[tex]\[
m = \frac{8 - (-4)}{-2 - 1}
\][/tex]
Simplify inside the parentheses:
[tex]\[
m = \frac{8 + 4}{-2 - 1}
\][/tex]
[tex]\[
m = \frac{12}{-3}
\][/tex]
Now, divide [tex]\( 12 \)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
m = -4
\][/tex]
Thus, the slope of the line containing points [tex]\( J \)[/tex] and [tex]\( K \)[/tex] is
[tex]\[
\boxed{-4}
\][/tex]
Therefore, the correct answer is A. -4.
