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?