Topic/Skill Definition/Tips
Topic: Proportion Example
1. Direct If two quantities are in direct proportion, as
Proportion one increases, the other increases by the
same percentage.
If y is directly proportional to x , this can be
written as y ∝ x
An equation of the form y=kx represents
direct proportion, where k is the constant
of proportionality.
2. Inverse If two quantities are inversely proportional,
Proportion as one increases, the other decreases by
the same percentage.
If y is inversely proportional to x , this can
1
be written as y ∝
x
k
An equation of the form y= represents
x
inverse proportion.
3. Using Direct: y = kx or y∝x p is directly proportional to q.
proportionality When p = 12, q = 4.
formulae k 1 Find p when q = 20.
Inverse: y = or y ∝
x x
1. p = kq
1. Solve to find k using the pair of values 12 = k x 4
in the question. so k = 3
2. Rewrite the equation using the k you
have just found. 2. p = 3q
3. Substitute the other given value from
the question in to the equation to find the 3. p = 3 x 20 = 60, so p = 60
missing value.
4. Direct Graphs showing direct proportion can be
Proportion written in the form y=k x n
with powers Direct proportion graphs will always start
at the origin.
Mr A. Coleman Glyn School
Topic: Proportion Example
1. Direct If two quantities are in direct proportion, as
Proportion one increases, the other increases by the
same percentage.
If y is directly proportional to x , this can be
written as y ∝ x
An equation of the form y=kx represents
direct proportion, where k is the constant
of proportionality.
2. Inverse If two quantities are inversely proportional,
Proportion as one increases, the other decreases by
the same percentage.
If y is inversely proportional to x , this can
1
be written as y ∝
x
k
An equation of the form y= represents
x
inverse proportion.
3. Using Direct: y = kx or y∝x p is directly proportional to q.
proportionality When p = 12, q = 4.
formulae k 1 Find p when q = 20.
Inverse: y = or y ∝
x x
1. p = kq
1. Solve to find k using the pair of values 12 = k x 4
in the question. so k = 3
2. Rewrite the equation using the k you
have just found. 2. p = 3q
3. Substitute the other given value from
the question in to the equation to find the 3. p = 3 x 20 = 60, so p = 60
missing value.
4. Direct Graphs showing direct proportion can be
Proportion written in the form y=k x n
with powers Direct proportion graphs will always start
at the origin.
Mr A. Coleman Glyn School
