Exploring Point Slope Form through Geogebra

In geometry we are studying parallel and perpendicular lines and the theorems that can be proven about them. In thinking about how to present the connection between algebra and geometry for this unit, I wanted to include an exploration of what exactly makes lines (and linear functions) so special: constant rate of change, or slope.

We did not get a chance to do this entire exploration in class, but I am expecting students to look at it at some point over the weekend. I know they have seen slope-intercept form, but point-slope form is convenient in many ways, especially in the way it applies the concept of slope between points located on a line.

Download my Geogebra file here.

Comments welcome!