To determine the slope of the line passing through the points [tex]\( J(6,1) \)[/tex] and [tex]\( K(-3,8) \)[/tex], we use the slope formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
where [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are the coordinates of the points. In our case:
[tex]\( J \)[/tex] has coordinates [tex]\((6, 1)\)[/tex] and [tex]\( K \)[/tex] has coordinates [tex]\((-3, 8)\)[/tex].
Substitute these coordinates into the slope formula:
[tex]\[
m = \frac{8 - 1}{-3 - 6}
\][/tex]
Simplify the numerator and the denominator:
[tex]\[
m = \frac{7}{-9}
\][/tex]
This simplifies to:
[tex]\[
m = -\frac{7}{9}
\][/tex]
So, the slope of [tex]\(\overleftrightarrow{JK}\)[/tex] is [tex]\(-\frac{7}{9}\)[/tex].
Hence, the correct answer is:
[tex]\[
\boxed{-\frac{7}{9}}
\][/tex]
