Final answer:
The slope of the line passing through the points (-4,-2) and (-4,22) is undefined because the line is vertical, indicated by the identical x-values of the points.
Step-by-step explanation:
The question asks us to determine the slope of the line that passes through the points (-4,-2) and (-4,22). To find the slope of a line, we normally use the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points the line passes through. However, in this case, we can see that the x-values for both points are the same: -4. This means that the line is vertical, and thus, the slope is undefined.
Here, the 'run' part of the rise over run calculation for slope is zero since the x-values are identical. Dividing by zero is not possible in mathematics, leading to an undefined value for the slope. So, the correct answer to the question is: