To find the slope of the line passing through the points \( J(1, -4) \) and \( K(-2, 8) \), we will use the slope formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Here, the points \( J \) and \( K \) are given as \( J(x_1, y_1) = (1, -4) \) and \( K(x_2, y_2) = (-2, 8) \).
Let's substitute the coordinates into the slope formula:
[tex]\[
m = \frac{8 - (-4)}{-2 - 1}
\][/tex]
Calculate the differences in the numerator and the denominator:
[tex]\[
m = \frac{8 + 4}{-2 - 1}
\][/tex]
[tex]\[
m = \frac{12}{-3}
\][/tex]
Simplify the fraction:
[tex]\[
m = -4
\][/tex]
So, the slope of the line passing through the points \( J(1, -4) \) and \( K(-2, 8) \) is \(-4\).
Therefore, the correct answer is:
A. [tex]\(-4\)[/tex]
