Prove that the line through the point (x1, y1) and parallel to the line Ax + By + C = 0 is A (x – x1) + B (y – y1) = 0.


Let the slope of line Ax + By + C = 0 be m


Ax + By + C = 0



m = -A/B


Equation of the line passing through point (x1, y1) and having slope is





A(x – x1) + B(y – y1) = 0


So, the line through point (x1, y1) and parallel to the line Ax + By + C = 0 is A (x – x1) + B (y – y1) = 0


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