To determine the slope of the line passing through the points [tex]\((-8, -5)\)[/tex] and [tex]\((-10, -9)\)[/tex], we need to follow these steps:
1. Identify the coordinates of the two points:
- Point 1: [tex]\((x_1, y_1) = (-8, -5)\)[/tex]
- Point 2: [tex]\((x_2, y_2) = (-10, -9)\)[/tex]
2. Calculate the change in [tex]\(y\)[/tex] (often denoted as [tex]\(\Delta y\)[/tex] or [tex]\(dy\)[/tex]):
[tex]\[
\Delta y = y_2 - y_1 = -9 - (-5) = -9 + 5 = -4
\][/tex]
So, the change in [tex]\(y\)[/tex] is [tex]\(-4\)[/tex].
3. Calculate the change in [tex]\(x\)[/tex] (often denoted as [tex]\(\Delta x\)[/tex] or [tex]\(dx\)[/tex]):
[tex]\[
\Delta x = x_2 - x_1 = -10 - (-8) = -10 + 8 = -2
\][/tex]
So, the change in [tex]\(x\)[/tex] is [tex]\(-2\)[/tex].
4. Determine the slope [tex]\(m\)[/tex], which is given by the formula:
[tex]\[
m = \frac{\Delta y}{\Delta x} = \frac{-4}{-2} = 2.0
\][/tex]
Hence, the slope of the line passing through the points [tex]\((-8, -5)\)[/tex] and [tex]\((-10, -9)\)[/tex] is [tex]\(2.0\)[/tex].
