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. The slope formula for a line passing through two 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 coordinates for points [tex]\( J \)[/tex] and [tex]\( K \)[/tex]:
- [tex]\( J(-1, -9) \)[/tex]
- [tex]\( K(5, 3) \)[/tex]
Let's denote:
- [tex]\( x_1 = -1 \)[/tex]
- [tex]\( y_1 = -9 \)[/tex]
- [tex]\( x_2 = 5 \)[/tex]
- [tex]\( y_2 = 3 \)[/tex]
Substitute these values into the slope formula:
[tex]\[
m = \frac{3 - (-9)}{5 - (-1)}
\][/tex]
Simplify the expression inside the numerator and the denominator:
[tex]\[
m = \frac{3 + 9}{5 + 1}
\][/tex]
[tex]\[
m = \frac{12}{6}
\][/tex]
Finally, divide the numerator by the denominator:
[tex]\[
m = 2
\][/tex]
Therefore, the slope of [tex]\(\overleftrightarrow{ JK }\)[/tex] is:
[tex]\[
\boxed{2}
\][/tex]
So, the correct answer is:
D. 2
