An enzyme is a physical machine present in limited amount. It must grab a substrate molecule, hold it as an enzyme-substrate complex, and only then turn it into product. Add more substrate and the rate climbs — until every enzyme is busy. Then it flattens at Vmax.
The substrate that gets you to exactly half of Vmax is KM, the Michaelis constant. Small KM means the enzyme hits half speed at low substrate — tighter apparent affinity. Vmax rises if you add enzyme; KM does not.
Plot 1/v against 1/[S] and the hyperbola straightens into a line. Its y-intercept is 1/Vmax and its x-intercept is −1/KM — that is the whole reason kineticists reach for the double-reciprocal plot.
A competitive inhibitor fights for the active site: it only looks like weaker binding, so apparent KM rises while Vmax holds — flood the bench with substrate and you win the race back. A noncompetitive one disables enzyme outright: Vmax falls, KM is untouched. Which parameter moves names the saboteur.
Something in the simulation stopped unexpectedly — the lesson continues without it. You can move on; nothing you did was wrong.