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?'
The lesson
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.
Watch it
Where it sits
Learn first
Nothing; this is a starting point.
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 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.