To determine the slope of the line passing through the 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 calculated as:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
For the points [tex]\( J(1, -4) \)[/tex] and [tex]\( K(-2, 8) \)[/tex]:
- [tex]\((x_1, y_1) = (1, -4)\)[/tex]
- [tex]\((x_2, y_2) = (-2, 8)\)[/tex]
Plug these values into the slope formula:
[tex]\[
m = \frac{8 - (-4)}{-2 - 1}
\][/tex]
Simplify the numerator and the denominator:
[tex]\[
= \frac{8 + 4}{-2 - 1}
\][/tex]
[tex]\[
= \frac{12}{-3}
\][/tex]
When we divide 12 by -3, we get:
[tex]\[
m = -4
\][/tex]
Thus, the slope of [tex]\(\overleftarrow{ JK }\)[/tex] is [tex]\(\boxed{-4}\)[/tex].
