Free Maths Calculator

Direct and Inverse Proportion Calculator

These questions link two quantities, x and y. You are told one matching pair, and asked for a new value. The fix is always the same: use the pair you know to find the constant k, write out the formula with k in it, then put the new x in. The k step is where the marks live.

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Method, Step by Step

    Worked Example

    y is directly proportional to x, and y = 6 when x = 2. Find y when x = 5.

    1. y = kx. Find k first:k = 6 ÷ 2 = 3
    2. Write the formula:y = 3x
    3. Use it:y = 3 × 5 = 15

    Answer: y = 15

    Try These Yourself

    y ∝ x and y = 20 when x = 4. Find y when x = 7.Show answerHide answer

    Answer: y = 35

    k = 5, so y = 5 × 7.

    y is inversely proportional to x, and y = 12 when x = 2. Find y when x = 6.Show answerHide answer

    Answer: y = 4

    k = 24, so y = 24 ÷ 6.

    y ∝ x² and y = 18 when x = 3. Find y when x = 5.Show answerHide answer

    Answer: y = 50

    k = 2, so y = 2 × 25.