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Finding k and the Equation

Part of Reciprocal Graphs — GCSE Mathematics

This deep dive covers Finding k and the Equation within Reciprocal Graphs for GCSE Mathematics. Revise Reciprocal Graphs in Graphs for GCSE Mathematics with 11 exam-style questions and 10 flashcards. This topic appears less often, but it can still be a useful differentiator on mixed-topic papers. It is section 5 of 11 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 5 of 11

Practice

11 questions

Recall

10 flashcards

Finding k and the Equation

For any point (x, y) on the curve y = k/x, the product xy = k is constant.

To find k if you are given a point on the curve:

  1. Substitute the coordinates into y = k/x
  2. Multiply both sides by x: k = xy
  3. Calculate k
  4. Write the full equation y = k/x

Example: A reciprocal graph passes through (3, 8). Find the equation.

k = xy = 3 × 8 = 24

Equation: y = 24/x

Check: when x = 6, y = 24/6 = 4. Product: 6 × 4 = 24 ✓

Keep building this topic

Read this section alongside the surrounding pages in Reciprocal Graphs. That gives you the full topic sequence instead of a single isolated revision point.

Understanding AsymptotesDrawing a Reciprocal Graph from a Table of ValuesCloser and Closer, but Never TouchingReciprocal Graph Essentials

Practice Questions for Reciprocal Graphs

The graph of y = 1/x has an asymptote along the x-axis. What does this mean?

  • A. The graph touches the x-axis at x = 0
  • B. The graph crosses the x-axis at x = 1
  • C. The graph gets closer and closer to the x-axis but never reaches it
  • D. The graph is a straight line along the x-axis
1 markfoundation

Explain why the graph y = 5/x has a vertical asymptote at x = 0 and a horizontal asymptote at y = 0.

2 markshigher

Quick Recall Flashcards

What does the graph of y = 1/x look like?
A hyperbola — two separate curved branches. - One branch in the top-right (positive x, positive y) - One branch in the bottom-left (negative x, negative y) The curve gets closer and closer to both axes but never touches them.
What is an asymptote and where are they on y = k/x?
An asymptote is a line the curve approaches but never reaches or crosses. For y = k/x: - Vertical asymptote: x = 0 (the y-axis) - The function is UNDEFINED when x = 0 - Horizontal asymptote: y = 0 (the x-axis) - y never equals zero for any finite x

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Understanding Asymptotes

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Drawing a Reciprocal Graph from a Table of Values