To find the slope of the line 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]
Let's identify the coordinates:
- Point [tex]\( J \)[/tex] has coordinates [tex]\( (x_1, y_1) = (6, 1) \)[/tex]
- Point [tex]\( K \)[/tex] has coordinates [tex]\( (x_2, y_2) = (-3, 8) \)[/tex]
First, calculate the difference in the [tex]\( y \)[/tex]-coordinates ([tex]\( \Delta y \)[/tex]):
[tex]\[
\Delta y = y_2 - y_1 = 8 - 1 = 7
\][/tex]
Next, calculate the difference in the [tex]\( x \)[/tex]-coordinates ([tex]\( \Delta x \)[/tex]):
[tex]\[
\Delta x = x_2 - x_1 = -3 - 6 = -9
\][/tex]
Now, substituting these differences into the slope formula:
[tex]\[
m = \frac{\Delta y}{\Delta x} = \frac{7}{-9} = -\frac{7}{9}
\][/tex]
Thus, the slope of the line passing through points [tex]\( J \)[/tex] and [tex]\( K \)[/tex] is [tex]\(-\frac{7}{9}\)[/tex].
The correct answer is:
B. [tex]\( -\frac{7}{9} \)[/tex]
