Why changing an equation moves a marble

A line such as y=-0.5x+3 has a gradient of −0.5. As x increases by one, y decreases by half a unit. In Rollgebra the same line becomes a physical surface.

What happens if you change the slope?

Changing -0.5 to -0.2 flattens the line. A marble encounters a shallower incline, so its path can change even when the starting point and targets stay in place. The actual result also depends on the simulation and where the marble makes contact.

What does the intercept do?

The +3 shifts the line vertically; it changes where a falling marble first contacts the track. This is a visual way to distinguish gradient from intercept without relying on memorised rules alone.

Try both equations in Formula Lab; the experiment is unscored.