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 (x1,y1) and parallel to the line Ax+By+C=0 is A(x-x1)+b(y-y1) = 0

Philoid · Accepted Answer

Any line parallel to Ax+By+C = 0 is Ax+By+K=0 – (1)

Now, (x1,y1) lies on it.

Therefore Ax1+By1+k=0 – (2)

From (1) and (2)

Ax+By = Ax1+By1

A(x-x1)+B(y-y1)=0 (Required equation)