To determine the slope of the line passing through the points [tex]\( J(-1, -9) \)[/tex] and [tex]\( K(5, 3) \)[/tex], we can use the slope formula:
[tex]\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Here, [tex]\((x_1, y_1)\)[/tex] represents the coordinates of point [tex]\( J \)[/tex] and [tex]\((x_2, y_2)\)[/tex] represents the coordinates of point [tex]\( K \)[/tex]. Substituting the given coordinates into the formula:
[tex]\[
\begin{aligned}
x_1 &= -1, & y_1 &= -9, \\
x_2 &= 5, & y_2 &= 3
\end{aligned}
\][/tex]
Using these values in the slope formula:
[tex]\[
\text{slope} = \frac{3 - (-9)}{5 - (-1)}
\][/tex]
Simplify the expressions in the numerator and denominator:
[tex]\[
\text{slope} = \frac{3 + 9}{5 + 1}
\][/tex]
This simplifies to:
[tex]\[
\text{slope} = \frac{12}{6}
\][/tex]
Finally, divide the values:
[tex]\[
\text{slope} = 2.0
\][/tex]
Therefore, the slope of the line passing through points [tex]\( J \)[/tex] and [tex]\( K \)[/tex] is [tex]\( \boxed{2.0} \)[/tex].
