Construct Proportion Equations

# Construct Proportion Equations

GCSE(H),

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

Write the relationship as either y prop x text( or ) y prop frac(1)(x).

Re-write the relationship as a formula:

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

Substitute any initial values into the equation (normally this will be to work out the constant of proportionality).

Perform any remaining calculations to calculate additional values.

## Examples

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.

Answer: f = 0.025d

f prop d

f = kd

2.5 = k xx 100

k = 2.5 ÷ 100 = 0.025

Therefore f = 0.025d

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