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
What a learner can do afterwards
- 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?'
1 · Read
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.
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.
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.
Equal ratios plot as one straight line through zero, so a proportion graph lets you read off any amount at a glance.
More to read
2: Introducing Proportional Relationships
Two quantities are in direct proportion when one is always the same multiple of the other. Three kilos at £2 per kilo cost £6, five kilos cost £10: the multiplier never changes. Tables show this as matching columns, where every output divided by its input gives the same number.
The unit value unlocks every question. Dividing £6 by 3 kg gives £2 per kilo, and multiplying out gives any amount. Finding the for-one value first is the most reliable route through ratio and proportion problems.
2.1: Representing Proportional Relationships with Tables
Tables test proportion at a glance: divide each output by its input and watch for a constant. The table 1 to 2, 2 to 4, 3 to 6 passes, because every row doubles. A table like 1 to 2, 2 to 3 fails, because the multiplier slips. One rogue row breaks direct proportion.
Missing table values come from the multiplier. Once you know each output is 2.5 times its input, any gap fills by multiplying. Tables, equations and graphs all carry the same multiplier, so learning one form teaches all three.
2.2: Representing Proportional Relationships with Equations
Every direct proportion has an equation of the form y = m times x, with no added constant. The apple prices follow cost = 2 times kilos. The number m is the unit rate, the gradient of the graph, and the table multiplier all at once.
Graphs of these equations are straight lines through the origin. Zero kilos cost £0, which is the point (0, 0), and every other point lines up from there. Reading a value off the line, like finding the cost of 5 kg, is the same calculation as the unit method, drawn.
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2 · Watch
En anglaisTake it off screen
Where it sits
Optional connections
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
17 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.