Inverse Variation Math Example 1

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Example 1

medium
\(y\) varies inversely with \(x\), and \(y = 8\) when \(x = 3\). Find \(k\) and the equation. Then find \(y\) when \(x = 6\).

Solution

  1. 1
    Inverse variation: \(y = k/x\), so \(k = xy\).
  2. 2
    \(k = 3 \times 8 = 24\).
  3. 3
    Equation: \(y = 24/x\).
  4. 4
    When \(x=6\): \(y = 24/6 = 4\).

Answer

\(k = 24\); \(y = 4\) when \(x = 6\)
In \(y = k/x\), as \(x\) doubles from 3 to 6, \(y\) halves from 8 to 4. The product \(xy = 24\) stays constant.

About Inverse Variation

A relationship where y=kxy = \frac{k}{x}: as one quantity doubles, the other halves—their product stays constant.

Learn more about Inverse Variation →

More Inverse Variation Examples

Example 2 hard

Speed and travel time are inversely proportional for a fixed distance. At 60 km/h the trip takes 4 h

Example 3 medium

If (y = k/x) and (y = 12) when (x = 5), find (y) when (x = 15).

Example 4 hard

The pressure (P) and volume (V) of a gas at constant temperature satisfy (PV = k). If (P = 4) atm wh

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