Proportion Equations

# Proportion Equations

GCSE(F), GCSE(H),

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. 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.

Similarly, for terms that are in inverse proportion:

y prop frac(1)(x)

can be re-written as

y = k xx frac(1)(x), text( or ) y = frac(k)(x)

## Examples

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

2. y is inversely proportional to x^2. When y = 3, x = 5. What is the value of x when y = 5? give your answer to 1 decimal place.

y prop frac(1)(x^2)
Therefore y = k frac(1)(x^2)
Substituting: 3 = frac(k)(5^2) and solve for k = 75
When y = 5, and using k = 75, 5 = frac(75)(x^2)
Rewrite as x^2 = frac(75)(5)
x^2 = 15 and solve for x = 3.873