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.
`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
`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