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,
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`
Using the equation above, what distance was travelled on 5 litres of fuel?
Substituting into the equation: `5 = 0.025 xx d`
`d = 200`
Answer: 200km