---
title: "Direct Proportion as a Formula"
description: "Write y = kx for two quantities in direct proportion, find k from one pair of values, and use the formula to predict others."
canonical: https://lightmysky.com/learn/mathematics/direct-proportion-as-a-formula-mt_nhSf9I7Bjz
source: https://lightmysky.com/learn/mathematics/direct-proportion-as-a-formula-mt_nhSf9I7Bjz.md
retrieved: 2026-09-12
---

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# Direct Proportion as a Formula

Write y = kx for two quantities in direct proportion, find k from one pair of values, and use the formula to predict others.

Subject: Mathematics · Area: Ratio & Proportion · Ages 14 to 15
Page: https://lightmysky.com/learn/mathematics/direct-proportion-as-a-formula-mt_nhSf9I7Bjz

## Ready when they can

- Find the constant of proportionality from one given pair
- Use the formula in both directions, from x to y and back
- Recognise direct proportion from a straight line through the origin

## Lesson: One rule links x and y

Two quantities are directly proportional when they change together at a steady rate. When x doubles, y doubles too, and when x triples, y triples too. That steady rate is the number k in the formula y equals k times x. A solution is just a pair that makes it true: with y equal to 3 times x, the pair 2 and 6 works, since 3 times 2 is 6.

One pair pins down the whole rule. Divide y by x to get k, since k never changes. With x equal to 4 and y equal to 20, k is 20 divided by 4, which is 5. With the pair 5 and 40, k is 40 divided by 5, which is 8.

**Example.** Once you know k, use the formula in either direction. Multiply by x to predict y: with k equal to 5 and x equal to 9, y is 45. Divide to go back: with k equal to 6 and y equal to 54, x is 54 divided by 6, which is 9.

**Tip.** Every direct proportion draws a straight line through the origin. In y equals k times x, putting x equal to 0 always gives y equal to 0. If a line misses the origin, or adds something or divides by x, it is not direct proportion.

**Recap.** Divide to find k, multiply to predict, and check the line runs through zero.

## Practice

18 questions on this page, each with its working shown.

## Needs first

- [Proportion](https://lightmysky.com/learn/mathematics/proportion-mt_5mIcmKRCgA)
- [Ratio Problems: Sharing, Changing and Combining](https://lightmysky.com/learn/mathematics/ratio-problems-sharing-changing-and-combining-mt_vJelayH4uv)

## Opens up

- [Rate Equations and Orders of Reaction](https://lightmysky.com/learn/science/rate-equations-and-orders-of-reaction-mt_1x3ogDKGxC)
- [Inverse Proportion](https://lightmysky.com/learn/mathematics/inverse-proportion-mt_ZbbN2x6tcL)