Slope Dynamics Visualizer
Slope is the single number that controls how a line sits on the page. This visualiser lets you drag m and watch the line pivot immediately, with presets that jump between the cases worth knowing.
How to use this simulation
- Drag the slope value m and watch the line respond
- Switch between preset lines and curves
- Read the rise and run off the grid
What to look for
- The line pivots about its y-intercept as m changes
- Steeper lines correspond to larger magnitudes of m, in either direction
- Parallel lines share a gradient; perpendicular gradients multiply to −1
The physics behind it
For a straight line y = mx + c, the gradient m is the rise over the run — the change in y for each unit change in x. Positive m tilts the line upwards, negative tilts it down, and m = 0 gives a horizontal line. A vertical line has no defined gradient, because the run is zero and the division is undefined.