---
title: "Proportion Graphs"
description: "Represent proportional relationships using double number lines (two parallel number lines aligned at 0) and ratio tables; recognise that equivalent ratios generate straight lines through the origin wh"
canonical: https://lightmysky.com/learn/mathematics/proportion-graphs-mt_FspV_imUGK
source: https://lightmysky.com/learn/mathematics/proportion-graphs-mt_FspV_imUGK.md
retrieved: 2026-10-19
---

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# Proportion Graphs

Represent proportional relationships using double number lines (two parallel number lines aligned at 0) and ratio tables; recognise that equivalent ratios generate straight lines through the origin when graphed

Subject: Mathematics · Area: Ratio & Proportion · Ages 11 to 14
Page: https://lightmysky.com/learn/mathematics/proportion-graphs-mt_FspV_imUGK

## Ready when they can

- Plot pairs of proportional values on a coordinate grid and draw the straight line through the origin
- Explain why a directly proportional relationship always passes through (0,0)
- Read a proportion graph to find an unknown value — e.g. 'If 3 kg costs £6, how much does 5 kg cost?'

## Lesson: Reading Proportion Graphs

When two amounts grow together at the same rate, they are directly proportional. A ratio table lists matching pairs side by side. If 1 cinema ticket costs £4, then 2 tickets cost £8, and 3 tickets cost £12. Every pair in the table follows the same rate.

*(drawing: The top of each bar rises by the same amount every time. That is the sign of a proportional relationship.)*

**Example.** To turn a ratio table into a graph, plot each pair as a point on a grid: (1, 4), (2, 8), (3, 12). Draw a straight line through these points, and it will also pass through (0, 0). Now you can read off any value without working it out again. If 3 tickets cost £12, follow the line across to 5 tickets: it costs £20.

**Tip.** A directly proportional graph always passes through (0, 0), because zero tickets always cost zero pounds. If a graph starts anywhere else on the vertical axis, the relationship is not directly proportional.

**Recap.** Equal ratios plot as one straight line through zero, so a proportion graph lets you read off any amount at a glance.

## Practice

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

## Needs first

- [Ratio and proportion vocabulary](https://lightmysky.com/learn/mathematics/ratio-and-proportion-vocabulary-mt_ESgc4YBw-a)
- [Coordinates (age 10+)](https://lightmysky.com/learn/mathematics/coordinates-age-10-mt_R4AY0LKxfl)
- [Ratio Notation](https://lightmysky.com/learn/mathematics/ratio-notation-mt_XWSGuFW7It)

## Opens up

- [Scale drawings and maps](https://lightmysky.com/learn/mathematics/scale-drawings-and-maps-mt_1badik7iKJ)
- [Proportion](https://lightmysky.com/learn/mathematics/proportion-mt_5mIcmKRCgA)
- [Compound Units](https://lightmysky.com/learn/mathematics/compound-units-mt_kLQOzZYrd5)
- [Ratio Notation and Relationships](https://lightmysky.com/learn/mathematics/ratio-notation-and-relationships-mt_yK51ZnKA8m)