To find the slope of the line passing through two points [tex]\( J(6, 1) \)[/tex] and [tex]\( K(-3, 8) \)[/tex], we use the slope formula. The slope [tex]\( m \)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here, the coordinates of the points are:
- [tex]\( J(6, 1) \)[/tex] meaning [tex]\( x_1 = 6 \)[/tex] and [tex]\( y_1 = 1 \)[/tex]
- [tex]\( K(-3, 8) \)[/tex] meaning [tex]\( x_2 = -3 \)[/tex] and [tex]\( y_2 = 8 \)[/tex]
Substitute these values into the slope formula:
[tex]\[ m = \frac{8 - 1}{-3 - 6} \][/tex]
Calculate the numerator and the denominator separately:
Numerator:
[tex]\[ 8 - 1 = 7 \][/tex]
Denominator:
[tex]\[ -3 - 6 = -9 \][/tex]
So, the slope is:
[tex]\[ m = \frac{7}{-9} = -\frac{7}{9} \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{B. -\frac{7}{9}} \][/tex]
