Sheet № 203 · Foundation + Higher · AQA · Edexcel · OCR
Direct Proportion Graphs –
Direct proportion graphs are tested across both Foundation and Higher GCSE Maths papers. Recognising a proportional relationship from a graph and finding the constant of proportionality are essential skills that link ratio, algebra, and graphical work.
§Key definitions
Question:
A graph shows the cost of apples. At 3 kg the cost is £4.50. Show that cost is directly proportional to weight and find the cost of 7 kg.
Answer:
(a) f = 0.08d (b) 9.6 litres (c) 125 km
Q1 (Foundation):
y is directly proportional to x. When x = 5, y = 15. Find y when x = 9.
Q2 (Foundation):
A graph passes through the origin and (4, 12). Write the equation.
Q3 (Higher):
The cost of ribbon is directly proportional to its length. 2.5 metres costs £3.75. Find the cost of 8 metres.
§Formulas to memorise
y = kx, where k is the constant of proportionality
k = y / x (for any point on the line other than the origin)
Calculate the constant of proportionality: k = y / x.
Write the equation as y = kx.
Worked example
A graph shows the cost of apples. At 3 kg the cost is £4.50. Show that cost is directly proportional to weight and find the cost of 7 kg.
Working:
⚠ Common mistakes
- ✗Assuming any straight line shows direct proportion. The line must pass through the origin. A line like y = 3x + 2 is linear but not directly proportional.
- ✗Using the origin to calculate k. Since 0/0 is undefined, always use a point where both x and y are non-zero.
- ✗Mixing up k and 1/k. If 5 litres costs £10, then k = 10/5 = 2 (cost per litre), not 5/10 = 0.5. Make sure you divide the y-value by the x-value.
✦ Exam tips
- →If the question says "directly proportional," immediately write y = kx and find k from the given information.
- →On graph questions, check that the line starts at (0, 0) before concluding direct proportion.
- →The constant k has real-world meaning — state it in context (e.g. "£2 per litre" or "0.08 litres per km").