Answer :
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]
[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]