Where two terms are in direct proportion to one another, it is written as
y∝x
where y and x are general terms; for example, x could be x3. It is said as y is in proportion to x. But if they are in direct proportion, then one is a multiple of another. This direct proportion can be re-written as:
y=kx
where k is a number called the constant of proportionality.
Given two values for x,y and k, the third value can be derived.
y is proportional to x. When y=30,x=10. What is the constant of proportionality?
y∝x
Re-write as y=kx
Substituting for y and x
30=k×10 and solve for k=3
Answer: 3
y is proportional to x2. When y=3,x=6. What is the value of x when y=6? Give your answer correct to two decimal places.
y∝(x2)
Therefore y=kx2
Substituting: 3=k(62) and solve for k=336=112
When y=6, and using k=112,
6=112x2
x=8.485=8.49 (2dp)
Answer: 8.49