To find the slope of the line passing through points [tex]\( J(1, -4) \)[/tex] and [tex]\( K(-2, 8) \)[/tex], we can 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:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Given the coordinates:
- Point [tex]\( J \)[/tex]: [tex]\( (1, -4) \)[/tex]
- Point [tex]\( K \)[/tex]: [tex]\( (-2, 8) \)[/tex]
We can identify:
- [tex]\( x_1 = 1 \)[/tex]
- [tex]\( y_1 = -4 \)[/tex]
- [tex]\( x_2 = -2 \)[/tex]
- [tex]\( y_2 = 8 \)[/tex]
Substituting these values into the formula, we get:
[tex]\[ m = \frac{8 - (-4)}{-2 - 1} \][/tex]
Simplifying inside the numerator and denominator:
[tex]\[ m = \frac{8 + 4}{-2 - 1} \][/tex]
[tex]\[ m = \frac{12}{-3} \][/tex]
[tex]\[ m = -4 \][/tex]
Therefore, the slope of the line passing through points [tex]\( J \)[/tex] and [tex]\( K \)[/tex] is [tex]\(\boxed{-4}\)[/tex], which corresponds to answer choice A.
