Describe how the position of a point can change when its coordinates are altered. For example, what happens if you move the point from (2, 3) to (2, -1)?

When you move a point from (2, 3) to (2, -1), you're changing the y-coordinate while keeping the x-coordinate the same. This means you’re moving the point straight down on the Cartesian plane. It's like lowering a flag on a flagpole; the flag stays at the same horizontal position but descends downwards. The new point (2, -1) is now 4 units below the original point (2, 3). Similarly, if you were to alter the x-coordinate instead, say from (2, 3) to (5, 3), you'd see a horizontal shift to the right. Imagine sliding a book across a table; while it retains its height, it can shift left or right depending on the coordinates you adjust. Each change in coordinates leads to a distinct movement on the graph, showcasing the visual nature of mathematical relationships.