What does it mean by a line being unique?
When a line is said to be unique, it means that there is only one line with that particular set of properties or characteristics. In the context of geometry or mathematics, a unique line refers to a line that is distinct and separate from all other lines.
To determine if a line is unique, you need to consider its defining characteristics. In Euclidean geometry, a line is uniquely determined by two points. That is, given any two distinct points, there exists exactly one line that passes through them. This unique line can be thought of as the straight path connecting those two points.
Another way to think about a unique line is by considering its equation. In coordinate geometry, a line is uniquely defined by its slope and y-intercept (or by its slope and any point on the line). The slope-intercept form of a line's equation, y = mx + b, represents a unique line if the values of m (the slope) and b (the y-intercept) are specific and not shared by any other line.
In summary, a line is said to be unique if it is distinct and separate from all other lines based on its defining properties, whether that be the points it passes through or the equation that represents it.