To determine the slope of the line passing through two points, we can use the slope formula. The formula to find the slope [tex]\( m \)[/tex] of a line passing through 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 points [tex]\( J(-1, -9) \)[/tex] and [tex]\( K(5, 3) \)[/tex]:
- [tex]\((x_1, y_1)\)[/tex] corresponds to the coordinates of point [tex]\( J \)[/tex], which are [tex]\((-1, -9)\)[/tex].
- [tex]\((x_2, y_2)\)[/tex] corresponds to the coordinates of point [tex]\( K \)[/tex], which are [tex]\((5, 3)\)[/tex].
Now, plug these values into the slope formula:
[tex]\[
m = \frac{3 - (-9)}{5 - (-1)}
\][/tex]
Simplify the numerator and the denominator:
[tex]\[
m = \frac{3 + 9}{5 + 1}
\][/tex]
Further simplification gives:
[tex]\[
m = \frac{12}{6}
\][/tex]
[tex]\[
m = 2
\][/tex]
Thus, the slope of the line [tex]\(\overleftrightarrow{ JK }\)[/tex] is [tex]\(\boxed{2}\)[/tex].
The correct answer is D.
