Select the correct answer.

Two points located on [tex]\(\overleftrightarrow{JK}\)[/tex] are [tex]\(J(6,1)\)[/tex] and [tex]\(K(-3,8)\)[/tex]. What is the slope of [tex]\(\overleftrightarrow{JK}\)[/tex]?

A. [tex]\(-\frac{9}{7}\)[/tex]

B. [tex]\(-\frac{7}{9}\)[/tex]

C. [tex]\(\frac{7}{9}\)[/tex]

D. [tex]\(\frac{9}{7}\)[/tex]



Answer :

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]