Slope Lab
Place two points on the grid with the sliders. Watch the slope triangle, the rise, the run, and the exact slope update live — then take on six make-a-slope challenges.
1 Place two points
Move the points. The dashed triangle shows the run (teal) and the rise (gold) between them; the slope is rise over run, simplified.
2 Make-a-slope challenges
Set the sliders so the slope between your two points matches the target, then press Check. All coordinates stay on the −8…8 grid.
3 What do you notice?
Move the points around and confirm each of these — they are the whole story of slope.
Swap which point you call “first”: the rise and run both flip signs, and the fraction is unchanged. What breaks the answer is subtracting in different orders top and bottom.
Line up the points vertically-ish and the slope blows up; make them nearly level and it shrinks toward 0. At exactly vertical, the run is 0 and the slope stops existing — that’s what “undefined” means.
Set a slope of 1/3 and the readout stays 1/3 — no 0.333333. Slope lives most honestly as a fraction.
Rise 3, run 36 — a wheelchair ramp. Rise 8, run 4 — a steep hill. Same formula, same idea: vertical change per horizontal change.