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Algebra · SS 1

Inverse variation

When one quantity doubles, the other halves (e.g. more workers, fewer days).

  • y ∝ 1x means y = kx

What the letters mean

y, x
the two quantities
k
the constant of variation

Worked example

y varies inversely as x, and y = 6 when x = 4. Find y when x = 8.

  1. Step 1: Find k

    6 = k4, so k = 24

  2. Step 2: Use y = 24x

    y = 248 = 3

Final answer: y = 3

See it

Play with this picture from the Direct and Inverse Variation lesson.

-6-6-5-5-4-4-3-3-2-2-1-1112233445566xyrun 2rise 4MA(0, 0)B(2, 4)

Gradient

2

rise ÷ run = 4 ÷ 2

Distance AB

2√5

≈ 4.47

Midpoint M

(1, 2)

average of A and B

Drag A and B (or focus one and use the arrow keys).