Proporção inversa y=k/x explorador | sinais & k

Q: How Devo 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.

Q: 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.

Q: 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.

Q: How Posso 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.

Pick your main Entrada

Constant k (fraction/decimal)

Examples: 6, -3, 1/2. y and xy update instantly.

Equation Entrada (y=k/x or xy=k)

Prefer fractions Teacher mode Quadrant guide Show asymptotes Tracer point Decimal places

k>0 (Quadrants I & III)

y = 6 / x

x and y Compartilhar the same sign → Quadrants I & III

xy = 6 (constant)

Como usar (3 passos rápidos)

Digite k (ou carregue um exemplo). Equação, tabela e gráfico sincronizam na hora.
Observe xy permanecer constante e veja quais quadrantes se destacam conforme o sinal de k.
Use o rastreador ou clique no gráfico no modo gráfico para definir k a partir de um ponto; depois exporte SVG/CSV ou copie a URL de compartilhamento.

Tabela (verificação de xy constante)

lista de x

x inicial passo Δx Linhas

x	y	xy	Check

xy deve corresponder a k em cada linha. x=0 não é permitido.

Dica: no modo Tabela → k, edite x e y; inferimos k a partir da primeira linha válida e marcamos linhas inconsistentes.

Gráfico (hipérbole e rastreador)

x do rastreador

O rastreador permanece em um lado de 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.

Compartilhar & export

Perguntas frequentes

How Devo 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 Posso check a table for inverse proportion?