Direct Variation

Definition

y varies directly as x means y = kx, where k is the constant of variation.

As x increases, y increases in the same ratio. Graph through origin.

Example: y varies directly as x. When x = 4, y = 10.
10 = k × 4   ⇒   k = 2.5
So y = 2.5x
When x = 7, y = 2.5 × 7 = 17.5

Other forms: y ∝ x² means y = kx². y ∝ √x means y = k√x.

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