Show that projection of a line from any finite point P onto

Show that projection of a line, from any finite point P , onto a parallel line is represented by a function of the form f (x) = ax+b .

Solution

For any fixed point P , the projection of a point onto a parallel line at distance b gets translated by distance b . f(x) = x + b

Any if both the parallel lines are fixed then the Projection gets increased or decreased by a factor of a . So , f(x) = a . Note : \"a\" and \"b\" are arbitrary constant .

Hence , combining the above two cases for a variable parallel line , the projection function follows the relation f(x) = ax + b