To determine the slope of the line passing through points [tex]\( J(6, 1) \)[/tex] and [tex]\( K(-3, 8) \)[/tex], we will use the formula for the slope ([tex]\( m \)[/tex]) of a line given 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]
Here, point [tex]\( J \)[/tex] has coordinates [tex]\((x_1, y_1) = (6, 1)\)[/tex] and point [tex]\( K \)[/tex] has coordinates [tex]\((x_2, y_2) = (-3, 8)\)[/tex].
First, we calculate the change in the y-coordinates (Δy):
[tex]\[ \Delta y = y_2 - y_1 = 8 - 1 = 7 \][/tex]
Next, we calculate the change in the x-coordinates (Δx):
[tex]\[ \Delta x = x_2 - x_1 = -3 - 6 = -9 \][/tex]
Now, substitute these values into the slope formula:
[tex]\[ m = \frac{\Delta y}{\Delta x} = \frac{7}{-9} = -\frac{7}{9} \][/tex]
Therefore, the slope of [tex]\( \overleftrightarrow{JK} \)[/tex] is [tex]\( -\frac{7}{9} \)[/tex].
The correct answer is:
B. [tex]\( -\frac{7}{9} \)[/tex]
