I don't usually write about math here and if you dislike math stop reading now, but I had an interesting interchange with one of my kids the other day. It concerned the the despised point-slope form of a linear equation, y - y1 = m(x - x1). I don't teach that form because (1) I find the distributive property to be a top-level producer of errors, and (2), you can't graph it on the calculator that way. In fact, the only way you can graph it without transforming it to slope-intercept form (which was I was taught to do in HS) is to plot the point and make a "slope triangle." What I teach kids to do is put the slope and coordinates of the point into y = mx + b and solve for b. Fewer steps and simpler.
My kid mentioned this to her teacher, who promptly flipped out. Apparently mine is a very old-fashioned way of doing this. It took me quite a while to figure out why someone would prefer that awkward form over the more commonly used one. I think it's about shifting. For all other kids of graphs, you learn how to shift them up and down, left and right, and equation form you use to do that is like point-slope form and has the same effect, shifting the line up and down, left and right. So it makes sense to do it that way except that although the form is similar and has the same effect, (1) the form is similar, but not identical (the standard form being y - k = f(x - h) or more commonly y = f(x-h) + k), and (2) I have NEVER seen a math teacher, or a math book for that matter, talk about point slope being about shifting lines. It wouldn't be a bad idea to do that, but they don't.
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