What it does
Two quantities are in direct proportion when doubling one doubles the other: twice as many pencils cost twice as much. They are in inverse proportion when doubling one halves the other: twice as many workers finish a job in half the days.
This page gives you four everyday situations, two of each kind. For each one it draws the graph and puts a dot on it that you drag left and right. As you drag, the page writes out the sum with your numbers, and a table of five rows shows the test:
- Direct: y ÷ x is the same in every row (the constant k), and the graph is a straight line through 0.
- Inverse: x × y is the same in every row (k again), and the graph is a curve that gets close to both axes but never touches them.
A slider changes k: the price of one pencil, the speed of the car, the total work in worker-days or the length of the trip.
It fits Class 8 Mathematics, proportional reasoning (direct and inverse proportion and the unitary method), and links forward to graphs of motion in Class 9 Science. Ratios themselves are mixed and compared in the ratio mixer; distance against time for a moving object is drawn live in motion graphs live.
How to use it
- Tap a situation: Pencils and cost or Time and distance (direct), Workers and days or Speed and time (inverse).
- Move the k slider, or type a value in the box, to change the constant.
- Drag the dot along the graph. The big line shows the pair of values; the line under it shows the sum.
- The highlighted column in the table is the one that stays the same.
A worked example
Workers and days with k = 24 worker-days (the job takes one worker 24 days):
- 4 workers: 24 ÷ 4 = 6 days.
- 8 workers: 24 ÷ 8 = 3 days. Twice the workers, half the days.
- The table rows 2 → 12, 4 → 6, 6 → 4, 8 → 3, 12 → 2 all have x × y = 24.
Pencils and cost with k = ₹5: 6 pencils cost 5 × 6 = ₹30, and every row has cost ÷ pencils = 5.
Unitary method for an inverse problem: 6 workers take 10 days, so the job is 6 × 10 = 60 worker-days, and 4 workers take 60 ÷ 4 = 15 days.
Check yourself
Four fresh questions each time: a direct cost problem, workers and days, speed and time, and spotting direct, inverse or neither from a table. Type the answer, press Check, and open the worked answer if you need it. Nothing is saved.
FAQ
Is “as one goes up, the other goes up” enough for direct proportion? No. y = x + 3 goes up with x, but y ÷ x changes, so it is not direct proportion. Its graph is a line that does not pass through 0.
Why does the inverse curve never touch the axes? x × y = k with k above 0, so neither x nor y can ever be 0. Zero workers would need endless days.
Is this from the NCERT book? It covers the same topic with fibub’s own pictures and examples. fibub is not part of NCERT.
Where the numbers come from
- Direct and inverse proportion, the unitary method and their graphs (a line through the origin and a rectangular hyperbola) are standard school mathematics. Wording, pictures and examples are fibub's own.
- Checked against hand-worked unitary-method examples (5 kg for ₹150 gives 8 kg for ₹240; 6 workers in 10 days gives 4 workers in 15 days).
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.