To determine the slope of the line that passes through the points (1, -6) and (-2, -8), we can follow a step-by-step approach:
### Step 1: Identify the Coordinates
Given points:
- Point 1 (x1, y1) = (1, -6)
- Point 2 (x2, y2) = (-2, -8)
### Step 2: Calculate the Change in y (Vertical Change)
The change in the y-coordinates (Δy) is found by subtracting the y-coordinate of the first point from the y-coordinate of the second point:
[tex]\[ \Delta y = y2 - y1 = -8 - (-6) = -8 + 6 = -2 \][/tex]
### Step 3: Calculate the Change in x (Horizontal Change)
The change in the x-coordinates (Δx) is found by subtracting the x-coordinate of the first point from the x-coordinate of the second point:
[tex]\[ \Delta x = x2 - x1 = -2 - 1 = -3 \][/tex]
### Step 4: Calculate the Slope
The slope of the line (m) is defined by the ratio of the change in y to the change in x:
[tex]\[ m = \frac{\Delta y}{\Delta x} = \frac{-2}{-3} = \frac{2}{3} \][/tex]
### Step 5: Write the Slope in Simplest Form
The slope is already in its simplest form as a fraction:
[tex]\[ m = \frac{2}{3} \][/tex]
Thus, the slope of the line that passes through the points (1, -6) and (-2, -8) is [tex]\(\boxed{\frac{2}{3}}\)[/tex].
