# Linear Function Geometry

You know, I was talking to a colleague yesterday and he was commenting on the ways that he is trying to keep skills from previous math classes fresh by integrating a variety of skill sets into the problems he assigns.

I liked that idea. I teach geometry and algebra both. Some of the geometry gets taught before Algebra I, so it get me thinking about ways I could combine the two in away that pushes the skill sets of both, but doesn’t have the same feel as the typical practice problem.

So, consider this: Plot four linear functions so that there is a triangle in each quadrant. The smallest triangle is in quadrant 1. The next biggest is in quadrant 2. The next biggest is in quadrant 3. The next biggest is in quadrant 4. Also, design your triangles in such a way that the area of the triangle in quadrant 1 is exactly half the area of the triangle in quadrant 3 and the area of the triangle in quadrant 2 is exactly half the area of the triangle in quadrant 4.

Once you have your triangles drawn, find the equations for the four functions you drew to create your triangles.

What could be the next steps in this problem? What can we do with the drawing that we have in front us? What do you think?