How to show that the equation of the line that passes through P1( x1, y1) and parallel to the line Ax+ By+ C= 0 is Ax +By = Ax1 + By1?

Question

How to show that the equation of the line that passes through P1( x1, y1) and parallel to the line Ax+ By+ C= 0 is Ax +By = Ax1 + By1? What steps should I do first?

Answer 1

First find the slope of the given line by solving for y. The coefficient of x will be the slope of that line and also any line that is parallel to that line.

Once you have the slope of the target line, you will have enough info to write the equation of the line passing through P₁. Use the point-slope formula then remove parentheses and transpose terms to show that the given equation is indeed a form for the target equation.

Once you have tried the above study the following to confirm:

desmos.com/calculator/6bp2r7tnac (note the sliders for A, B, C and x₁, y₁, along with the fact that there are multiple forms for each line.