Final answer:
The slope of the line passing through the points (-1,1) and (-1,4) is undefined because the line is vertical, indicated by the x-coordinates being the same.
Step-by-step explanation:
The slope of a line that passes through the points (-1,1) and (-1,4) is determined by calculating the change in y-coordinates divided by the change in x-coordinates. Since the x-coordinates are the same (both -1), the slope is calculated as follows:
Change in y: 4 - 1 = 3
Change in x: -1 - (-1) = 0
Since dividing by zero is undefined, we conclude that the line is vertical, and therefore, the slope is undefined. A vertical line does not have a defined slope because it does not run diagonally or horizontally; it runs straight up and down.