To determine the slope of the line that passes through the points [tex]\( J(6,1) \)[/tex] and [tex]\( K(-3,8) \)[/tex], we use the formula for the slope of a line given by 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, we can assign:
- [tex]\( x_1 = 6 \)[/tex]
- [tex]\( y_1 = 1 \)[/tex]
- [tex]\( x_2 = -3 \)[/tex]
- [tex]\( y_2 = 8 \)[/tex]
Let's proceed step by step:
1. Calculate the difference in the [tex]\( y \)[/tex]-coordinates:
[tex]\[
y_2 - y_1 = 8 - 1 = 7
\][/tex]
2. Calculate the difference in the [tex]\( x \)[/tex]-coordinates:
[tex]\[
x_2 - x_1 = -3 - 6 = -9
\][/tex]
3. Substitute these differences into the slope formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7}{-9} = -\frac{7}{9}
\][/tex]
Thus, the slope of the line [tex]\(\overleftrightarrow{J K}\)[/tex] is [tex]\(-\frac{7}{9}\)[/tex].
Now, let’s compare this result with the provided options:
A. [tex]\(-\frac{9}{7}\)[/tex]
B. [tex]\(-\frac{7}{8}\)[/tex]
C. [tex]\(\frac{7}{9}\)[/tex]
D. [tex]\(\frac{9}{7}\)[/tex]
The correct answer is:
- None of the provided answers directly correspond to [tex]\(-\frac{7}{9}\)[/tex]
Therefore, there seems to be an error in the provided answer choices or an additional context might be needed to reflect the correct answer, but based on the calculation, the slope of the line through [tex]\(J(6,1)\)[/tex] and [tex]\(K(-3,8)\)[/tex] is [tex]\(-\frac{7}{9}\)[/tex].
