To determine the slope of the line that passes through the points [tex]\((-5, -5)\)[/tex] and [tex]\( (5, -7) \)[/tex], follow these steps:
1. Identify the coordinates:
- First point [tex]\((x_1, y_1) = (-5, -5)\)[/tex]
- Second point [tex]\((x_2, y_2) = (5, -7)\)[/tex]
2. Use the slope formula:
The formula for 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]
3. Substitute the coordinates into the formula:
- [tex]\(y_2 - y_1 = -7 - (-5)\)[/tex]
- [tex]\(x_2 - x_1 = 5 - (-5)\)[/tex]
4. Simplify the differences:
- [tex]\(y_2 - y_1 = -7 + 5 = -2\)[/tex]
- [tex]\(x_2 - x_1 = 5 + 5 = 10\)[/tex]
5. Calculate the slope:
[tex]\[
m = \frac{-2}{10} = -0.2
\][/tex]
Since [tex]\(-0.2\)[/tex] is equivalent to [tex]\(-\frac{1}{5}\)[/tex], the slope of the line is [tex]\(-\frac{1}{5}\)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{A. -\frac{1}{5}}
\][/tex]
