Construct Proportion Equations

## Construct Proportion Equations

To construct proportion equations from a description, first identify whether the relationship is a direct proportion or an indirect proportion.

If the the relationship is in direct proportion, write the equation as y prop x

Re-write the relationship as a formula, changing prop to an equals and multiplying one side by a constant of proportionality k:

y = kx

The x term might be a power term.

Normally you will be given an initial pair of values, and asked to complete a second pair of values. Work out the constant of proportionality first, which will allow you to work out the second pair,

## Example 1

On one particular journey, the amount of fuel (f) used by a car was directly proportional to the distance (d) travelled. Over a distance of 100km, 2.5 litres of fuel was used.

Find a formula for f in terms of d.

f prop d

f = kd

2.5 = k xx 100

k = 0.025

Therefore f = 0.025d

Answer: f = 0.025d

## Example 2

Using the equation above, what distance was travelled on 5 litres of fuel?

Substituting into the equation: 5 = 0.025 xx d

d = 200