Direct and Indirect Proportion

What is Direct Proportion?

• If a quantity ‘A’ is directly proportional to another quantity ‘B’, this means that if ‘A’ increases, then ‘B’ increases by the same amount • The ratio of A:B is unchanged

Direct Proportion Example

• The cost of petrol depends on the number of litres you buy. If you buy 0l then the cost will be R0.

• The litres is the independent variable• The cost is the dependent variable

Try this…• A performer sells his CDs for R80. His income equals:y = 80x

where y is the cost and x the number of CD’s

Complete the table to represent the relationship.Nr of CDs

1 2 3 4 5 10

Income 80

Nr of CDs

1 2 3 4 5 10

Income 80 160 240 320 400 800

The Answer…

Now let’s graph it:

0 1 2 3 4 5 60

50100150200250300350400450

Direct proportion graph of cost of CD sales

Number of CD’s

Pric

e in

Ran

ds

What is Indirect Proportion?

• If a quantity ‘A’ is inversely proportional to another quantity ‘B’, then as ‘A’ increases ‘B’ decreases by the same amount.

Indirect Proportion Example

• Speed (S) vs Time (T)

Speed is inversely proportional to time; if you double your speed (S x 2), then you halve the time (T x ½) it takes to travel the same distance.

Try this…• A school hires a bus for R420. It takes a maximum of 80

passengers. Complete the table to represent the relationship.

• To calculate the cost per person, we can say:y = 420 ÷ x

where y is the cost pp and x the number of people

Nr of People

10 20 30 40 50 80

Cost p/p 42

The Answer…

Nr of People

10 20 30 40 50 80

Cost p/p 42 21 14 10,50 8,40 5,25

Now let’s graph it:

5 10 15 20 25 30 35 40 45 50 5505

1015202530354045

Indirectly proportional graph on cost per person for the bus trip

Number of people

Cost

per

per

son