Slope of a Line Segment between Two Points in Three Dimensions
The geometric intuition for a slope is or our rise for every unit that we move.
Example: Find the slope of the segment from (1, 1, 0) to (4, 5, 6).
Solution:
- Find the run: The run is between (1, 1, 0) and (4, 5, 0) in the xy
Using Pythagoras, we can conclude that the run is 5.
- Find the rise:
The rise is the distance from (4, 5, 0) to (4, 5, 6) is 6.
- To visualize the slope we are obtaining, place the right triangle with vertices (1, 1, 0), (4, 5, 0), and (4, 5, 6) in 3-space.
- The slope is