To find the slope of a line passing through two points, we use the slope formula:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Given the points [tex]\((-6, -8)\)[/tex] and [tex]\((-1, -7)\)[/tex], we can identify the coordinates as follows:
- [tex]\((x_1, y_1) = (-6, -8)\)[/tex]
- [tex]\((x_2, y_2) = (-1, -7)\)[/tex]
Substituting these coordinates into the slope formula, we get:
[tex]\[ \text{slope} = \frac{-7 - (-8)}{-1 - (-6)} \][/tex]
Simplify the expressions inside the parentheses:
[tex]\[ \text{slope} = \frac{-7 + 8}{-1 + 6} \][/tex]
This simplifies to:
[tex]\[ \text{slope} = \frac{1}{5} \][/tex]
Thus, the slope of the line passing through the points [tex]\((-6, -8)\)[/tex] and [tex]\((-1, -7)\)[/tex] is:
[tex]\[ \frac{1}{5} \][/tex]
Therefore, the slope in reduced fraction form is [tex]\( \frac{1}{5} \)[/tex].
