To find the slope of the line [tex]\(\overleftrightarrow{JK}\)[/tex] passing through the points [tex]\( J(6, 1) \)[/tex] and [tex]\( K(-3, 8) \)[/tex], we use the formula for the slope [tex]\( m \)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
First, identify the coordinates of points [tex]\( J \)[/tex] and [tex]\( K \)[/tex]:
- [tex]\( J \)[/tex]: [tex]\( (x_1, y_1) = (6, 1) \)[/tex]
- [tex]\( K \)[/tex]: [tex]\( (x_2, y_2) = (-3, 8) \)[/tex]
Next, 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]
Since the negative sign can be placed either in the numerator or the denominator, it simplifies to:
[tex]\[
m = -\frac{7}{9}
\][/tex]
Thus, the slope of the line [tex]\(\overleftrightarrow{JK}\)[/tex] is:
[tex]\[
m = -\frac{7}{9}
\][/tex]
The correct answer is:
B. [tex]\(-\frac{7}{9}\)[/tex]
