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

## 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)