How to Find the Equation of a Parallel Line in 4-5 Lines of Work (Shorter Version)

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 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 how to identify where the gradient's information is 'stored' in a linear equation, and use that information to show how to simplify the entire process to just 4-5 lines of (simple) work!

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