To find the slope of the line passing through the points [tex]\( J(1, -4) \)[/tex] and [tex]\( K(-2, 8) \)[/tex], we'll use the slope formula:
[tex]\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Where [tex]\( (x_1, y_1) \)[/tex] and [tex]\( (x_2, y_2) \)[/tex] are the coordinates of the points [tex]\( J \)[/tex] and [tex]\( K \)[/tex], respectively.
Let's assign the coordinates as follows:
[tex]\[
(x_1, y_1) = (1, -4)
\][/tex]
[tex]\[
(x_2, y_2) = (-2, 8)
\][/tex]
Now we substitute these values into the slope formula:
[tex]\[
\text{slope} = \frac{8 - (-4)}{-2 - 1}
\][/tex]
Simplify the numerator and the denominator:
[tex]\[
\text{slope} = \frac{8 + 4}{-2 - 1} = \frac{12}{-3}
\][/tex]
Finally, divide 12 by -3:
[tex]\[
\text{slope} = -4
\][/tex]
Therefore, the correct answer is:
A. -4
