Sure! Let's find the slope of the line passing through the points [tex]\((-4, 1)\)[/tex] and [tex]\((4, -5)\)[/tex].
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 the formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Given the points [tex]\((-4, 1)\)[/tex] and [tex]\((4, -5)\)[/tex], we can identify:
[tex]\[
(x_1, y_1) = (-4, 1)
\][/tex]
[tex]\[
(x_2, y_2) = (4, -5)
\][/tex]
Plug these values into the slope formula:
[tex]\[
m = \frac{-5 - 1}{4 - (-4)} = \frac{-5 - 1}{4 + 4} = \frac{-6}{8}
\][/tex]
Simplify the fraction:
[tex]\[
m = \frac{-6}{8} = \frac{-3}{4}
\][/tex]
Therefore, the slope of the line passing through these points is:
[tex]\[
-\frac{3}{4}
\][/tex]
Thus, the correct answer is:
[tex]\[
\boxed{-\frac{3}{4}}
\][/tex]
