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.

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Solution

The slope of line Ax + By + C = 0 or is

It is known that parallel lines have the same slope.

∴ Slope of the other line =

The equation of the line passing through point (x₁, y₁) and having a slope is

Hence, the line through point (x₁, y₁) and parallel to line Ax + By + C = 0 is

A (x –x₁) + B (y – y₁) = 0

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