To find the slope of the line passing through points [tex]\( G(-2, 6) \)[/tex] and [tex]\( H(5, -3) \)[/tex], we use the slope formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Here, [tex]\((x_1, y_1) = (-2, 6)\)[/tex] and [tex]\((x_2, y_2) = (5, -3)\)[/tex]. Substituting these coordinates into the slope formula, we get:
[tex]\[
m = \frac{-3 - 6}{5 - (-2)}
\][/tex]
First, perform the subtraction in both the numerator and the denominator:
[tex]\[
m = \frac{-3 - 6}{5 + 2}
\][/tex]
This simplifies to:
[tex]\[
m = \frac{-9}{7}
\][/tex]
Thus, the slope of the line [tex]\( \overleftrightarrow{GH} \)[/tex] is:
[tex]\[
-\frac{9}{7}
\][/tex]
Therefore, the correct answer is:
[tex]\[
-\frac{9}{7}
\][/tex]
