Direct Proportion

In a Nutshell

Two quantities are in direct proportion when one is always a fixed multiple of the other. If one doubles, the other doubles too.

When two quantities are directly proportional, their ratio stays the same:

y=k×xy = k \times x

Here kk is the constant of proportionality (the multiplier). For example, if 1 pencil costs 30p then 2 pencils cost 60p, 3 cost 90p, and so on. The cost is always 30 times the number of pencils.

You can spot direct proportion because the ratio yx\dfrac{y}{x} is the same for every pair of values.

Direct proportion as a straight line through zero A table of x and y values on the left, a graph on the right. Points sit on a straight line through the origin, showing that y equals k times x.
Scenario:

Choose a scenario and watch the points line up through the origin. Press "Double x" to see that doubling one quantity doubles the other.

Watch it work

Question: 4 notebooks cost £6. How much do 10 notebooks cost?

Have a go

Q1. 3 apples cost 90p. How much do 7 apples cost?

Q2. A car uses 8 litres of petrol to travel 96 miles. How far can it travel on 5 litres?

Q3. 5 identical books weigh 1.5 kg. How much do 12 books weigh?

Q4. A tap fills a bucket with 6 litres in 2 minutes. How long does it take to fill 15 litres?