If \(y\) is directly proportional to \(x\), then when \(x\) is multiplied by a number, \(y\) is multiplied by the same number.
The number of miles covered is directly proportional to the time spent walking.
If 5 miles are covered in 2 days, how many miles will be covered in 7 days?
17.5 miles are covered in 7 days.
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.
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.
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?
It takes 8 men 5 days.
If \(y\) is directly proportional to \(x^2\),
then when \(x\) is multiplied by a number, \(y\) is multiplied by the square of that number.
The distance moved by an accelerating car is directly proportional to the square of the time of acceleration.
After 2 seconds, the car has travelled 12 m. What is the distance travelled after 9 seconds?
The car has travelled 243 m.
\(y\) varies as \(x^2\) and inversely as \(z\).
Given \(y = 12\) when \(x = 6\) and \(z = 9\), find \(y\) when \(x = 10\) and \(z = 15\).
So \(y = 20\).