2 for linear (powers of 1), 3 for quadratic (powers of 2), etc
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A point lies on a line if the coordinates of the point satisfy the equation of the line.
Yes its on the line.
A single point cannot determine the slope of a straight line. It can, therefore, have any slope at all.
Yes since 3 non-collinear points determine a plane. Of course one can take any two of the three points and draw a line between them. There are an infinite number of planes going through this line. Now pick on more point, not on the line, and those three points uniquely determine a plane.
Two distinct (different) points are needed to determine a line.