Final answer:
The slope of a line through the points (-4, -6) and (-4, -8) is undefined because it represents a vertical line, which means there is no run (horizontal change) to calculate the rise over.
Step-by-step explanation:
The slope of a line through two points can be found by calculating the "rise over run", which means the difference in the y-coordinates (the rise) divided by the difference in the x-coordinates (the run). Specifically, for the points (-4, -6) and (-4, -8), the slope calculation would be:
Slope (m) = (y2 - y1) / (x2 - x1) = (-8 - (-6)) / (-4 - (-4)) = (-2) / (0).
Since division by zero is undefined, this indicates that we have a vertical line, which means the slope is undefined. Vertical lines have slopes that are not numerically expressible since they do not have a run (horizontal change).