We know that dimensions depend on degree of freedom. For example any line $ax+by+c=0$ in 2D plane is 1 dimensional because if I know the $x$ or $y$ value, we calculate the $y$ or $x$ value. That's why the line has dimension $1$. But many places are saying that line is $2$ dimensional, I am very confused by this, what is right?
2026-04-04 05:21:09.1775280069
Does a line have 2 degrees of freedom or 1 degree of freedom?
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You are confused because these are different things.
To pick a point from the set of points on a given line: one degree of freedom (by the argument you give)
To pick a line from the set of lines in a plane: two degrees of freedom (e.g., its direction and its distance from the origin; or: pick two points in the plane = 4 degrees, but subtract 2 degrees because their position on the line is irrelevant; or ...)
To pick a line from the set of lines in 3d space: four degrees of freedom (why?)