Using Transformation of Lines to Teach Writing y=mx+b

I am probably super late to the game for thinking about this, but why don't we teach our older kids to write linear equations using the concept of transformation of a graph?? Especially because they seem to have so much trouble remembering to plug in a point to solve for b, and we keep teaching the same method over and over every year.

Here are my Do Now questions for the day (as warm up for writing simple piecewise function equations, which the kids did wonderfully with!). We have seen absolute value equations/transformations this year but haven't covered quadratic transformations yet.

1.) How do the graphs of y = |x| and y = |x - 3| + 5 differ? Be specific.

2.) Try to write the equation of a quadratic function with vertex at (-1, -9) and standard steepness/shape. Simplify your equation as much as possible.

3.) Using the same idea, write an equation of a linear function of slope 8, that passes through (-16, 7). Simplify your equation as much as possible.

4.) All 3 of the above are related concepts. How??

It turned out to be a super nice lead-in to piecewise functions; kids were whipping up linear equations left and right (correctly) and actually focusing in on the domain-restriction aspect of the task. YES! Small victories!!