To find the slope of the line that passes through the points [tex]\((-4, 1)\)[/tex] and [tex]\((4, -5)\)[/tex], we use the formula for 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]:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Let's use the given points [tex]\((-4, 1)\)[/tex] and [tex]\((4, -5)\)[/tex]:
1. [tex]\(x_1 = -4\)[/tex], [tex]\(y_1 = 1\)[/tex]
2. [tex]\(x_2 = 4\)[/tex], [tex]\(y_2 = -5\)[/tex]
Substitute these values into the slope formula:
[tex]\[
m = \frac{-5 - 1}{4 - (-4)}
\][/tex]
First, simplify the numerator:
[tex]\[
-5 - 1 = -6
\][/tex]
Next, simplify the denominator:
[tex]\[
4 - (-4) = 4 + 4 = 8
\][/tex]
Now we can calculate the slope:
[tex]\[
m = \frac{-6}{8}
\][/tex]
Simplify the fraction:
[tex]\[
m = -\frac{6}{8} = -\frac{3}{4}
\][/tex]
Therefore, the correct answer is:
[tex]\[
-\frac{3}{4}
\][/tex]
