To determine the slope of the line passing through the points [tex]\((-2, 5)\)[/tex] and [tex]\((4, -4)\)[/tex], we'll use the slope formula for a line given two points, [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here, the coordinates of the points are:
- [tex]\(x_1 = -2\)[/tex]
- [tex]\(y_1 = 5\)[/tex]
- [tex]\(x_2 = 4\)[/tex]
- [tex]\(y_2 = -4\)[/tex]
Plug these values into the slope formula:
[tex]\[
\text{slope} = \frac{-4 - 5}{4 - (-2)}
\][/tex]
Simplify the numerator and the denominator:
[tex]\[
\text{slope} = \frac{-4 - 5}{4 + 2} = \frac{-9}{6}
\][/tex]
Further simplify the fraction:
[tex]\[
\text{slope} = \frac{-9}{6} = -\frac{3}{2}
\][/tex]
Thus, the slope of the line containing the points [tex]\((-2, 5)\)[/tex] and [tex]\((4, -4)\)[/tex] is [tex]\(-\frac{3}{2}\)[/tex].
The correct answer is:
[tex]\[ \boxed{-\frac{3}{2}} \][/tex]
