Proportion Portal
Two portals, two rules: direct proportion (y = kx, a line through the origin) and inverse (y = k/x, a falling curve). Find k, write the equation, and use it — the grade-9 way, every time.
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Proportion Portal 🌀
Two quantities can be linked in two opposite ways. In **direct** proportion they grow together; in **inverse** proportion, as one grows the other shrinks. Both follow the same reliable script: write the relationship with a constant **k**, use a known pair to find k, then use the equation. Step through both portals.
Direct proportion 📈
**y is directly proportional to x** (written y ∝ x) means **y = kx** for some constant k. Double x and you double y; treble x and you treble y. Its graph is a **straight line through the origin** — no intercept, because when x = 0, y = 0.
Which is direct proportion?
In which situation is one quantity DIRECTLY proportional to the other?
- The total cost of apples and the number of apples bought
- The time to finish a job and the number of workers on it
- A person's age and their height
- The outdoor temperature and the month of the year
Find the constant k 🔑
Every proportion question turns on finding **k**. Substitute a known pair: If y is directly proportional to x, and **y = 12 when x = 3**, then 12 = k × 3, so **k = 4**. The full equation is **y = 4x** — now you can find y for any x, or x for any y.
Find k
An interactive activity.
Order the method
An interactive activity.
Use the equation
An interactive activity.
Plot the next point
An interactive activity.
Inverse proportion 🔄
**y is inversely proportional to x** (y ∝ 1/x) means **y = k ÷ x**. Now as x **doubles**, y **halves** — they move in opposite directions. A handy consequence: **x × y = k** stays constant. The graph is a falling **reciprocal curve**, never a straight line.
Which is inverse proportion?
Which situation shows INVERSE proportion?
- The number of workers on a job and the time it takes to finish
- The number of hours worked and the total pay earned
- The number of litres of petrol and the amount paid
- The day of the week and the temperature
Find k for inverse
An interactive activity.
Use the inverse equation
An interactive activity.
The two portals
When y is directly proportional to x, the equation is y = _____, and its graph is a straight line through the _____. When y is inversely proportional to x, the equation is y = k ÷ x, and as x increases, y _____.