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.

Question

Prove that the line through the point (x 1 , y 1 ) and parallel to the line Ax + By + C = 0 is A (x – x 1 ) + B (y – y 1 ) = 0.

Philoid · Accepted Answer

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

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.