Yesterday, the Pre-Algebra students did some practice problems dealing with the graphing of linear equations. We went over how to pick values, plug them in, find coordinates and graph the line. I tossed the equations into Desmos for them to check.
Today, I put up two equations at a time and asked them to make observations.
All 3 sections pretty quickly noticed that the equations all ended in numbers and the lines intersected the y-axis at that number.
"Do you think this is a coincidence, or do you think it will work for all of them? According to your theory, where will this one hit?"
Through the power of Desmos, I was able to hide and show various equations to test their theory.
"What else do you notice? How could we describe how these lines look?"
We had a lengthy discussion about positive and negative slope and what that means. We talked about the implications of the number in front of the x in the equation and what happens to the line as that number changes.
There were some EXCELLENT questions that I wasn't quite ready to answer that involved the nature of vertical and horizontal lines.
"If the slope gets higher as the number gets bigger, would a vertical line be one where that number is infinity?"
Heck yes, kid!
I didn't ask them to produce anything but their thoughts and they came through amazingly well.