Proportion equations · Year 12

In Year 12 you learn: proportion to powers and roots.

When two quantities are in proportion, you can write a formula linking them, find the constant k from one pair of values, and then use the formula for any other value. Many science laws — springs, gravity, light — are proportion formulas.

Key facts

• y ∝ x means y = kx; y ∝ x² means y = kx²; y ∝ √x means y = k√x.
• y ∝ 1/x means y = k/x; y ∝ 1/(x²) means y = k/(x²).
• Method: write the formula with k. Put in the pair you know to find k. Then use the formula.
• Direct: y ÷ x stays the same (straight-line graph through the origin). Inverse: x × y stays the same.
• If y ∝ xⁿ and x is multiplied by s, y is multiplied by sⁿ. For y ∝ 1/(x²), doubling x divides y by 4.

Worked examples

Other years

• Proportion equations · Year 10
• Proportion equations · Year 11