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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`

Answer: 200km