How can we explain equations for lines through the origin?
1) Play with the buttons to see what they do!
2) Put the third (alpha) button in the 0 degree position.
3) Put the second button C in a fixed position, and vary the first X button to a bunch of different values. Answer and discuss:
How many of the X cm strip does it take to make the Y cm strip exactly?
What does C tell you about how X and Y are related?
See if you can write and explain an equation that relates X and Y.
4) Now move the third (alpha) button to the 90 degree position and repeat part 3.
5) Repeat parts 2, 3, and 4 but with a different fixed value for C.
6) Continue to repeat parts 2, 3, and 4 with different fixed values for C.
7) Discuss: what kinds of equations do lines through (0,0) have and why do they have that kind of equation?