"semi-graphical" solving of linear equations

A word about the title of this applet - The sliders change the graphs of f(x) and g(x) but not by direct manipulation. The blue, red and green sliders move the blue, red and green dots vertically. The black sliders allow for scaling and translating both functions. All five sliders change at least one of the functions. Some of the sliders change both functions. Which sliders change one function? Which sliders change both functions? What is the effect of each of the sliders on the symbolic expression for f(x)? for g(x)?