To find the slope of the line segment [tex]\(\overrightarrow{JK}\)[/tex] passing through the points [tex]\( J(-1, -9) \)[/tex] and [tex]\( K(5, 3) \)[/tex], we use the slope formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Here, [tex]\((x_1, y_1)\)[/tex] is the point [tex]\(J(-1, -9)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is the point [tex]\(K(5, 3)\)[/tex]. Substituting these coordinates into the slope formula, we get:
[tex]\[
m = \frac{3 - (-9)}{5 - (-1)}
\][/tex]
Simplify the terms in the numerator and the denominator:
[tex]\[
m = \frac{3 + 9}{5 + 1}
\][/tex]
This simplifies to:
[tex]\[
m = \frac{12}{6}
\][/tex]
Further simplifying the fraction gives us:
[tex]\[
m = 2
\][/tex]
Therefore, the correct answer is:
D. 2
