Final answer:
The slope of a line passing through (-9, -2) and (-9, -6) is not defined because the line is vertical, displaying no horizontal change between the two points.
Step-by-step explanation:
The slope of a line is calculated by the difference in y-coordinates divided by the difference in x-coordinates, often referred to as “rise over run”. The formula for slope is as follows:
m = (y2 - y1) / (x2 - x1)
Where m is the slope, (x1, y1) and (x2, y2) are coordinates of two points on the line.
In this case, we have the two points (-9, -2) and (-9, -6). Plugging these into the formula, we get:
m = (-6 - (-2)) / (-9 - (-9))
m = (-6 + 2) / (-9 + 9)
m = -4 / 0
This identifies that we have a line where the change in x is 0, meaning that the line is vertical. Since division by zero is undefined, a vertical line does not have a slope. In more practical terms, it can be considered to have an infinite slope, but this is a concept rather than a number we can work with algebraically.