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Math · Graphs

Proporção inversa y=k/x com sinais, quadrantes e constante xy

Um explorador interativo que mantém a equação y=k/x, a tabela e o gráfico em sincronia. Veja xy=k permanecer constante, alternar quadrantes quando k muda de sinal, visualizar assíntotas, pontos de rastreamento, verificações de consistência de tabela e exportar/compartilhar para ensino.

A sample is loaded automatically. All calculations stay in your browser; nothing is sent to a server.

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Pick your main input

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)

Como usar (3 passos rápidos)

  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

How do I find the constant of inverse proportion?

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

Which quadrants does the graph appear in?

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.

Why is x=0 not allowed?

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

Why doesn’t the curve cross the axes?

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

How can I check a table for inverse proportion?

Calcular 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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