Example

Finding the Direct Variation Equation Given y=20y = 20 When x=8x = 8

Problem: If yy varies directly with xx and y=20y = 20 when x=8x = 8, find the equation that relates xx and yy.

Step 1 — Write the direct variation formula: y=kxy = kx

Step 2 — Substitute the given values: Replace yy with 2020 and xx with 88: 20=k820 = k \cdot 8

Step 3 — Solve for the constant of variation: Divide both sides by 88: 208=k\frac{20}{8} = k k=2.5k = 2.5

Step 4 — Write the equation: Substitute k=2.5k = 2.5 back into the general formula: y=2.5xy = 2.5x

The equation relating xx and yy is y=2.5xy = 2.5x.

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Updated 2026-04-21

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