To determine the slope of the line that contains the points [tex]\((-5, -4)\)[/tex] and [tex]\((-3, -5)\)[/tex], we can utilize the slope formula:
[tex]\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
where [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are the coordinates of the two points. For this problem, let [tex]\((x_1, y_1) = (-5, -4)\)[/tex] and [tex]\((x_2, y_2) = (-3, -5)\)[/tex].
1. Calculate the change in [tex]\( y \)[/tex] (denoted as [tex]\(\Delta y\)[/tex]):
[tex]\[
\Delta y = y_2 - y_1 = -5 - (-4) = -5 + 4 = -1
\][/tex]
2. Calculate the change in [tex]\( x \)[/tex] (denoted as [tex]\(\Delta x\)[/tex]):
[tex]\[
\Delta x = x_2 - x_1 = -3 - (-5) = -3 + 5 = 2
\][/tex]
3. Compute the slope by dividing the change in [tex]\( y \)[/tex] by the change in [tex]\( x \)[/tex]:
[tex]\[
\text{slope} = \frac{\Delta y}{\Delta x} = \frac{-1}{2} = -\frac{1}{2}
\][/tex]
Thus, the slope of the line that passes through the points [tex]\((-5, -4)\)[/tex] and [tex]\((-3, -5)\)[/tex] is:
[tex]\[
-\frac{1}{2}
\][/tex]
Therefore, the correct answer is:
[tex]\[
-\frac{1}{2}
\][/tex]
