The algebra of lines with perpendicular gradients

Author:
Greg Drury
The red and blue lines are at right angles - perpendicular. Play the animation and observe the gradient values. The relationship can be described as "negative inverse".
  1. What is the general equation of the red line?
  2. How could you express the "negative inverse" relationship using algebra?
  3. What is the general equation of the blue line?
  4. Given that the slider moves at a constant rate, why does the rotation accelerate and slow down in the animation?