To find the slope of the line that goes through the points [tex]\((-5, -5)\)[/tex] and [tex]\( (5, -7) \)[/tex], we use the slope formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here, [tex]\((x_1, y_1)\)[/tex] are the coordinates of the first point, and [tex]\((x_2, y_2)\)[/tex] are the coordinates of the second point. Plugging in the given points, we have:
[tex]\[
(x_1, y_1) = (-5, -5) \\
(x_2, y_2) = (5, -7)
\][/tex]
Now, substitute these values into the slope formula:
[tex]\[ m = \frac{-7 - (-5)}{5 - (-5)} \][/tex]
Simplify the numerator and the denominator:
[tex]\[ m = \frac{-7 + 5}{5 + 5} \][/tex]
[tex]\[ m = \frac{-2}{10} \][/tex]
Simplify [tex]\(\frac{-2}{10}\)[/tex]:
[tex]\[ m = -0.2 \][/tex]
Therefore, the slope of the line that goes through [tex]\((-5, -5)\)[/tex] and [tex]\( (5, -7) \)[/tex] is [tex]\( -0.2 \)[/tex].
Looking at the answer choices, the slope of [tex]\( -0.2 \)[/tex] corresponds to the fraction:
[tex]\[ -0.2 = -\frac{1}{5} \][/tex]
Thus, the correct answer is:
A. [tex]\(-\frac{1}{5}\)[/tex]
