To find the slope of the line that contains the points [tex]\((2, -8)\)[/tex] and [tex]\((-4, 4)\)[/tex], you can use the slope formula. The slope [tex]\( m \)[/tex] between 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]
Plugging in the coordinates of the given points:
- [tex]\((x_1, y_1) = (2, -8)\)[/tex]
- [tex]\((x_2, y_2) = (-4, 4)\)[/tex]
Substituting these values into the formula:
[tex]\[
m = \frac{4 - (-8)}{-4 - 2}
\][/tex]
Simplify the numerator and the denominator:
[tex]\[
m = \frac{4 + 8}{-4 - 2} = \frac{12}{-6}
\][/tex]
Then, simplify the fraction:
[tex]\[
m = \frac{12}{-6} = -2
\][/tex]
Thus, the slope of the line that contains the points [tex]\((2, -8)\)[/tex] and [tex]\((-4, 4)\)[/tex] is [tex]\(-2\)[/tex].
So, the correct answer is:
[tex]\[
-2
\][/tex]
