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For two main reasons.

The first reason is that, depending on the information that is available to you (two points, a point and slope, slope and intercept) one or the other form is easier to find.

The second reason is that different forms are "better" in different situations. The slope and intercept are parameters that have very obvious interpretations in 2-dimensional geometry. In 3-d, however, they don't make such obvious sense.

The general form: ax + by + cz = k where a, b, c and k are constants is a line in 3-dimensional space. It is easily converted to 2-d (just remove the z term) or extended to 4-dimensions (add a "dw" term where d is a constant and w another variable). Extension to 5 or more dimensions is done similarly.

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12y ago

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