When considering how many lines can pass through one given point, it’s essential to differentiate between the two scenarios: one point alone versus two points.
For one given point, an infinite number of lines can pass through it. This is because you can draw a line at any angle around that point, and there is no limit to the number of such lines you can draw.
In the case of two given points, precisely one line can connect them. The geometric principle here is unique; any two distinct points define exactly one straight line. However, if we include the first point in this scenario and consider it as a separate point, the first point does not change the outcome. You can still draw only one line that passes through the two given points and this line will also pass through the additional given point if aligned with it.
In summary, through one given point, there are infinitely many lines, while through two given points, there is exactly one line.