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Proportion inverse y=k/x : signes, quadrants et produit xy constant

Visualisez les asymptotes, suivez les points et vérifiez la cohérence du tableau pendant que k change.

Un exemple est chargé automatiquement. Tous les calculs restent dans votre navigateur.

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Examples: 6, -3, 1/2. y and xy update instantly.
k>0 (Quadrants I & III)
y = 6 / x
x and y share the same sign → Quadrants I & III
xy = 6 (constant)

Comment l’utiliser (3 étapes rapides)

  1. Enter k (or load an example). Equation, table, and graph sync immediately.
  2. Watch xy stay constant and see which quadrants light up based on the sign of k.
  3. Use Tracer or click the graph in Graph mode to set k from a point, then export SVG/CSV or copy the share URL.

Table (xy constant check)

xyxyCheck
xy should match k in every row. x=0 is not allowed.

Tip: in Table → k mode, edit x and y; we infer k from the first valid row and flag inconsistent rows.

Graph (hyperbola & tracer)

Tracer stays on one side of x=0.

What this shows

  • xy=k stays constant: any valid point (x,y) satisfies xy=k. Doubling x halves y.
  • Quadrants flip by sign: k>0 lives in Quadrants I & III; k<0 lives in Quadrants II & IV.
  • x=0 is forbidden: division by zero causes the vertical asymptote at x=0; y=0 is also an asymptote when k≠0.
  • Tracer & point→k: move along one branch or click in Graph mode to set k from a point.
  • Precision: fractions stay exact internally; decimals are rendered for readability.

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FAQ

Comment trouver la constante de proportion inverse ?

Multiply x and y: k=xy. One point determines k, and all rows or tracer points should keep the same product.

Dans quels quadrants le graphe apparaît-il ?

k>0 goes to Quadrants I and III (same sign). k<0 goes to Quadrants II and IV (different signs). The highlighted guide shows this.

Pourquoi x=0 n’est-il pas autorisé ?

Inverse proportion divides by x. x=0 would be division by zero, shown as a vertical asymptote on the graph.

Pourquoi la courbe ne coupe-t-elle pas les axes ?

For k≠0 the curve approaches x=0 and y=0 but never meets them. Only k=0 would sit on the axes.

Comment vérifier un tableau pour une proportion inverse ?

Compute xy for each row. If all products match the same k and x is never 0, it fits y=k/x. Inconsistent rows are highlighted.

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