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Proportion Equations

Proportion Equations

Where two terms are in direct proportion to one another, it is written as

`y prop x`

where `y` and `x` are general terms; for example, `x` could be `x^3`. It is said as `y` is in proportion to `x`. But if they are in direct proportion, then one is a multiple of another. This direct proportion can be re-written as:

`y = kx`

where `k` is a number called the constant of proportionality.

Given two values for `x, y text( and ) k`, the third value can be derived.

Example 1

`y` is proportional to `x`. When `y = 30, x = 10`. What is the constant of proportionality?

`y prop x`

Re-write as `y = kx`

Substituting for `y text( and ) x`

`30 = k xx 10` and solve for `k = 3`

Answer: 3

Example 2

`y` is proportional to `x^2`. When `y = 3, x = 6`. What is the value of `x` when `y = 6`? Give your answer correct to two decimal places.

`y prop (x^2)`

Therefore `y = kx^2`

Substituting: `3 = k(6^2)` and solve for `k = frac(3)(36) = frac(1)(12)`

When `y = 6`, and using `k = frac(1)(12)`,

`6 = frac(1)(12)x^2`

`x = 8.485 = 8.49` (2dp)

Answer: 8.49