These sometimes come up on the exam – so don’t forget about them!
If two quantities are in direct proportion then when one increases or decreases the other increases or decreases by the same percentage.
On a graph this is shown with a straight line through the origin: y = kx
As one quantity increases the other one decreases.
The equation and graph for this is y = k/x
Proportional to can be shown by the symbol .
Examiners might throw in some nasty looking proportions so here’s some examples of what you might expect.
y is proportional to x squared -> y x²
y is proportional to x cubed -> y x³
y is proportional to the square root of x -> y √x
y is inversely proportional to x cubed -> y 1/x³
In an exam you will probably need to change the proportion into an equation to work something out. To do so just change the proportional sign to an =k – here’s some examples to show you what we mean
y x² becomes y = kx²
y x³ becomes y = kx³
y √x becomes y = k√x
y 1/x³ becomes y = k/x³
So What Sort Of Question Will I Be Asked On This Topic?
Let’s take an example!
Example: y is inversely proportional to x. When x = 12, y = 3. Find the constant proportionality and find x when y = 8.
First write down the proportionality. Here it is inverse proportion so
Replace the sign with an =k
y = k/x
You can then manipulate the equation like normal
So xy = k
Put in the values from the question
3 x 12 = 36
So k = 36
So the constant proportionality is 36…so now you can find x when y = 8
8x = 36
so x = 4.5