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Inverse proportion y=k/x with signs, quadrants, and xy constant

An interactive explorer that keeps the equation y=k/x, the table, and the graph in sync. See xy=k stay constant, switch quadrants when k changes sign, visualize asymptotes, tracer points, table consistency checks, and export/share for teaching.

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)

How to use (3 quick steps)

  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.

Share & export

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?

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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