2. Direct Proportion
• If ‘a’ is proportional to ‘b’ then as b increases,
a increases – which can be written as a b.
• In fact, there is a constant number ‘k’ with the
formula a = kb.
• The value of k will be the same for all values of
a and b and so it can be found by substituting
in the a and b values.
3. Steps to solve proportion problems
1. Write equation using given values (e.g. a =kb)
2. Rearrange the equation to find the value of k
(the constant).
3. Hence, write a new equation, substituting k
with given values to answer the question.
4. Example 1
• y is proportional to z
• y = 7 when z = 2
• Find the value of y when z = 8
• y = kz 7 = k x 2
• k = 7 ÷ 2 = 3.5
• k = 3.5z
• y = 3.5 x 8 =
= 28
5. Example 2
• y is directly proportional to x.
• x = 30 and y = 45
• Find y when x = 40.
• y = kx
• 45 = k x 30 therefore k = 45 ÷ 30
• k = 1.5
• y = 1.5 x 40 =
= 60
6. Example 3
• t is directly proportional to u.
• t = 24 when u = 8
• Find t when u = 7
• t = ku
• 24 = k x 8 therefore k = 24 ÷ 8
• k = 3
• t = 3 x 7 =
= 21
