To determine the slope of the line passing through the points [tex]\( J(1, -4) \)[/tex] and [tex]\( K(-2, 8) \)[/tex], we follow these steps:
1. Identify the coordinates of the points:
- Point [tex]\( J \)[/tex] has coordinates [tex]\( (1, -4) \)[/tex].
- Point [tex]\( K \)[/tex] has coordinates [tex]\( (-2, 8) \)[/tex].
2. Recall the formula to calculate the slope [tex]\( m \)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
3. Substitute the coordinates of points [tex]\( J \)[/tex] and [tex]\( K \)[/tex] into the formula:
- [tex]\( x_1 = 1 \)[/tex], [tex]\( y_1 = -4 \)[/tex]
- [tex]\( x_2 = -2 \)[/tex], [tex]\( y_2 = 8 \)[/tex]
[tex]\[
m = \frac{8 - (-4)}{-2 - 1}
\][/tex]
4. Simplify the numerator and the denominator:
- Numerator: [tex]\( 8 - (-4) = 8 + 4 = 12 \)[/tex]
- Denominator: [tex]\( -2 - 1 = -3 \)[/tex]
5. Compute the slope by dividing the numerator by the denominator:
[tex]\[
m = \frac{12}{-3} = -4.0
\][/tex]
Thus, 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. -4
