To find the slope of the line passing through the points [tex]\( J(1, -4) \)[/tex] and [tex]\( K(-2, 8) \)[/tex], we use the slope formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Here, [tex]\( (x_1, y_1) = (1, -4) \)[/tex] and [tex]\( (x_2, y_2) = (-2, 8) \)[/tex].
Plugging in these coordinates into the formula:
[tex]\[
m = \frac{8 - (-4)}{-2 - 1}
\][/tex]
Simplify the numerator and the denominator:
[tex]\[
m = \frac{8 + 4}{-2 - 1} = \frac{12}{-3}
\][/tex]
Now simplify the fraction:
[tex]\[
m = -4
\][/tex]
Hence, the slope of the line passing through points [tex]\( J \)[/tex] and [tex]\( K \)[/tex] is [tex]\(-4\)[/tex].
Therefore, the correct answer is:
A. [tex]\(-4\)[/tex]
