Direct proportion

 

If y is directly proportional to x,

then when x is multiplied by a number so is y.

    

Example

 

The number of miles covered is directly proportional to the time spent walking.

If 5 miles is covered in 2 days, how many miles will be covered in 7 days ?

 

17.5 miles is covered in 7 days.

 

Example

The cost of bricks is directly proportional .

Fred buys 10 bricks for £5.

George buys 5 bricks for £2.50

How much does Harry pay for 18 bricks ?

Harry pays £9 for 18 bricks.

 

Indirect proportion

If y is indirectly proportional to x, then
when x is multiplied by a number,
 y is divided by that number, and vice versa. 

As one number goes up, the other goes down.

                   

 

Example

The number of days taken to dig a ditch is inversely proportional to the number of men digging.

If it takes 4 days for 10 men to dig a trench, how long will it take 8 men to dig the trench ?

It takes 8 men 5 days.

 

 

Squared proportion

If y is directly proportional to x²,

then when x is multiplied by a number,

y is multiplied by the square of that number.

 

 

Example

The distance moved by an accelerating car is directly proportional to the square of the amount of time of acceleration.

After 2 seconds, the car has travelled a distance of 12 m.

What is the distance travelled by the car after 9 seconds ?

 

The car has travelled 243 m.

 

Joint Variation

Example

y varies as x² and inversely as z.

Given y = 12 when x = 6 and z = 9,
Find y when x = 10 and z = 15