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. 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]
For the given points, [tex]\((x_1, y_1) = (-5, -5)\)[/tex] and [tex]\((x_2, y_2) = (5, -7)\)[/tex], we can substitute these values into the formula to find the slope.
First, calculate the difference in the [tex]\(y\)[/tex]-coordinates:
[tex]\[
y_2 - y_1 = -7 - (-5) = -7 + 5 = -2
\][/tex]
Next, calculate the difference in the [tex]\(x\)[/tex]-coordinates:
[tex]\[
x_2 - x_1 = 5 - (-5) = 5 + 5 = 10
\][/tex]
Now, substitute these differences into the slope formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2}{10} = -\frac{1}{5}
\][/tex]
Therefore, the slope of the line that goes through [tex]\((-5, -5)\)[/tex] and [tex]\((5, -7)\)[/tex] is [tex]\(-\frac{1}{5}\)[/tex].
The correct answer is:
A. [tex]\(-\frac{1}{5}\)[/tex]
