Proportion summary

Key learning points

• Direct: $y=kx$; inverse: $y=\frac{k}{x}$.
• Find $k$ from given values, then predict new values.
• Tables of values: check ratios $y/x$ (direct) or products $xy$ (inverse).

Worked example 1 — Direct proportion

$y\propto x$. When $x=4$, $y=10$. Find $y$ when $x=6$.

Working

$y=kx$ with $k=2.5$.

Worked example 2 — Inverse proportion

$y\propto\tfrac{1}{x}$. When $x=2$, $y=12$. Find $y$ when $x=8$.

Working

$xy$ constant.

Worked example 3 — Recipe scaling

Recipe for 4 needs $300\,\mathrm{g}$. For 10?

Working

Scale by $\tfrac{10}{4}$.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.