Final Answer:
a. The line passing through the points (6,-4) and (6,2) is vertical, parallel to the y-axis.
Step-by-step explanation:
a. The points (6,-4) and (6,2) both share the same x-coordinate, which is 6. In a Cartesian coordinate system, when two points have the same x-coordinate, the line passing through them is vertical and parallel to the y-axis. Therefore, line is vertical and parallel to the y-axis.
Understanding the geometry of lines based on their coordinates is fundamental in mathematics. When points share the same x-coordinate, the resulting line is vertical, and when points share the same y-coordinate, the line is horizontal. Recognizing these patterns allows for quick visual interpretation of the orientation of lines in a coordinate system.
In summary, the line passing through the points (6,-4) and (6,2) is vertical, indicating that all points on this line have the same x-coordinate of 6. This vertical orientation is a characteristic feature when points share the same x-coordinate, providing a straightforward way to determine the direction of lines in the coordinate plane.