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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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How to use this calculator effectively

This calculator is designed to make scenario checks fast. Use a repeatable workflow: baseline first, one variable change at a time, then compare output direction and magnitude.

How it works

Run your first scenario with defaults. Then, change exactly one assumption and observe which result changes most. That is the fastest way to identify sensitivity and explain what drives the outcome.

When to use

Use this page when you need practical planning support, side-by-side alternatives, or a clean baseline for further discussion.

Common mistakes to avoid

Worked example

Prepare a base case and one alternative case, then compare outputs and validate the direction, scale, and interpretation with the same assumptions across both cases.

See also

How to use Inverse proportion y=k/x with signs, quadrants, and xy constant effectively

What this calculator does

This page is for estimating outcomes by changing inputs in one controlled workflow. The model keeps your focus on variables, not output shape. Start with stable assumptions, then test sensitivity by changing one key input at a time to observe directional impact.

Input meaning and unit policy

Each input has an expected unit and a typical range. For reliable interpretation, check whether you are using the same unit system, period, and base assumptions across all runs. Unit mismatch is the most common source of unexpected drift in numeric results.

Use-case sequence

A practical sequence is: first run with defaults, then create a baseline log, then run one alternative scenario, and finally compare only the changed output metric. This sequence reduces cognitive load and prevents false pattern recognition in early experiments.

Common mistakes to avoid

Avoid changing too many variables at once, mixing incompatible data sources, and interpreting a one-time output without checking robustness. A single contradictory input can flip conclusions, so keep each experiment minimal and document assumptions as part of your note.

Interpretation guidance

Review both magnitude and direction. Direction tells you whether a strategy moves outcomes in the desired direction, while magnitude helps you judge practicality. If both agree, you can proceed; if not, rebuild the baseline and verify constraints before deciding.

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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