To find the slope of the line passing through the points [tex]\((-6, 6)\)[/tex] and [tex]\((4, -7)\)[/tex], you can use the slope formula. The slope [tex]\( m \)[/tex] of a line passing through 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 two points are:
[tex]\[
(x_1, y_1) = (-6, 6)
\][/tex]
[tex]\[
(x_2, y_2) = (4, -7)
\][/tex]
Substituting these values into the slope formula, we get:
[tex]\[
m = \frac{-7 - 6}{4 - (-6)}
\][/tex]
First, calculate the numerator [tex]\((y_2 - y_1)\)[/tex]:
[tex]\[
y_2 - y_1 = -7 - 6 = -13
\][/tex]
Next, calculate the denominator [tex]\((x_2 - x_1)\)[/tex]:
[tex]\[
x_2 - x_1 = 4 - (-6) = 4 + 6 = 10
\][/tex]
So, the slope [tex]\( m \)[/tex] is:
[tex]\[
m = \frac{-13}{10} = -1.3
\][/tex]
Therefore, the slope of the line passing through the points [tex]\((-6, 6)\)[/tex] and [tex]\((4, -7)\)[/tex] is [tex]\(\boxed{-1.3}\)[/tex].
