To find the slope of the line passing through the points [tex]\( A(-2, 6) \)[/tex] and [tex]\( B(4, 5) \)[/tex], we can use the slope formula:
[tex]\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Here, [tex]\((x_1, y_1) = (-2, 6)\)[/tex] and [tex]\((x_2, y_2) = (4, 5)\)[/tex].
Now, substitute the given values into the slope formula:
[tex]\[
\text{slope} = \frac{5 - 6}{4 - (-2)}
\][/tex]
First, calculate the difference in the y-coordinates:
[tex]\[
5 - 6 = -1
\][/tex]
Now, calculate the difference in the x-coordinates:
[tex]\[
4 - (-2) = 4 + 2 = 6
\][/tex]
Finally, divide the difference in the y-coordinates by the difference in the x-coordinates:
[tex]\[
\text{slope} = \frac{-1}{6}
\][/tex]
Therefore, the slope of line [tex]\( AB \)[/tex] is [tex]\( \frac{-1}{6} \)[/tex].
