A little background: the previous lesson was writing linear equations given a point and the slope and using vertex form y=m(x-h)+k to do that.
I display the first example for the class:
Me: "Class, I'm confused. There is no slope, and how do I know which point to use for (h, k) since there are two?"
Student: "What if we use one point as (h, k) and the other as (x, y)?"
This is totally not what I was expecting. I always teach my students to use the slope formula
(y2-y1)/(x2-x1), but this is super that a student was thinking and brave enough to risk being wrong.
Me: "I like what you are thinking. So, which one is (h, k) and which one is (x, y)?"
The class decided to try both to see what happens. At this point I'm ready to pass out with excitement.
Once we saw that you would get the same result, I asked them if there were any other ways to find the slope. One students suggested the slope formula. Yay!
After that, I allowed students to decide what method they liked best.
BTY the equation is y = 2x + 3