To find the slope of the line that passes through two points [tex]\( J(-1, -9) \)[/tex] and [tex]\( K(5, 3) \)[/tex], you can use the slope formula:
[tex]\[
\text{slope} = \frac{{y_2 - y_1}}{{x_2 - x_1}}
\][/tex]
Here, the coordinates of point [tex]\( J \)[/tex] ([tex]\( x_1, y_1 \)[/tex]) are [tex]\(-1, -9\)[/tex] and the coordinates of point [tex]\( K \)[/tex] ([tex]\( x_2, y_2 \)[/tex]) are [tex]\(5, 3\)[/tex].
Substitute the given coordinates into the formula:
[tex]\[
\text{slope} = \frac{{y_2 - y_1}}{{x_2 - x_1}} = \frac{3 - (-9)}{5 - (-1)}
\][/tex]
Simplify inside the numerator and the denominator:
[tex]\[
\text{slope} = \frac{3 + 9}{5 + 1} = \frac{12}{6}
\][/tex]
Finally, divide the numerator by the denominator to find the slope:
[tex]\[
\text{slope} = \frac{12}{6} = 2
\][/tex]
Therefore, the slope of [tex]\( \stackrel{\rightharpoonup}{JK} \)[/tex] is [tex]\( 2 \)[/tex].
The correct answer is:
D. [tex]\( 2 \)[/tex]
