So often, we make calculations more difficult than they need be. This is very true of the way in which we find the equations of lines parallel to a given line through some given point.
So that students understand that the two parallel lines will have the same gradient, we teach them to rearrange a linear equation into the gradient-intercept form first ... and then (often) convert it back to some other form at the end of the process. This 'double conversion' is useful in driving home the principle that parallel lines have identical gradients, but it is terribly wasteful and inefficient if you simply want to find the final equation!
In this video I show you how to identify where the gradient's information is 'stored' in a linear equation. I then show you how to use that knowledge to simplify the entire calculation to just 4-5 lines of (simple) work!
Elementary-Intermediate: If you are new to calculating the equations for parallel lines, please watch this longer video (26:44):
Advanced: If you already know how to perform this calculation the conventional way, and would like to see the simpler format, then you might like to watch this shorter video (12:24):