Direct Proportion
𝑦 is directly proportional to 𝑥.
Complete the table below.
𝑥
−5
−2
0
−14
𝑦
2
𝑦 is directly proportional to 𝑥.
𝑦 is 24 when 𝑥 is 36.
Find a formula linking 𝑥 and 𝑦.
5
𝑉 is directly proportional to the square of 𝑙.
Rob says that when 𝑙 is doubled, the value of
𝑉 is multiplied by 2. Is Rob correct? Give
reason for your answer.
Correct
35
Sketch a graph on the axis that shows y is
directly proportional to 𝑥.
𝑦 is directly proportional to 𝑥 2
Work out the value of 𝑎.
𝑦
𝑥
𝑥
4
𝑎
𝑦
80
180
Incorrect
The length of a baby is directly proportional
to its weight. An average baby measures
50cm and has a weight of 2.5kg. Estimate
the weight of a baby measuring 48cm long.
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Direct Proportion
𝑦 is directly proportional to 𝑥.
Complete the table below.
𝑥
−5
−2
𝑦
-35 −14
𝑦 is directly proportional to 𝑥.
𝑦 is 24 when 𝑥 is 36.
Find a formula linking 𝑥 and 𝑦.
0
2
5
0
14
35
×7
Sketch a graph on the axis that shows y is
directly proportional to 𝑥.
𝑦
y𝛼𝑥
𝑦𝛼 𝑥
𝑦=𝑘 𝑥
24 = 𝑘 36
24 = 6𝑘
24
𝑘=
=4
6
𝑦 is directly proportional to 𝑥 2
Work out the value of2𝑎.
180 = 5𝑎2
𝑦𝛼𝑥
6
𝑥 4
180
𝑦 = 𝑘𝑥 2
2
𝑎 =
2
5
80
=
𝑘
×
4
180
𝑦
2
𝑎
=
36
80 = 16𝑘
𝑎 = 36
80
𝑘=
=5 𝑎=6
16
Therefore
𝑦 = 5𝑥 2 and 𝑎 = 6
80
𝑥
Therefore
𝑦=4 𝑥
𝑉 is directly proportional to the square of 𝑙.
Rob says that when 𝑙 is doubled, the value of
𝑉 is multiplied by 2. Is Rob correct? Give
reason for your answer.
Correct
Incorrect
Rob is wrong, because V𝛼𝑙2 so 𝑉 = 𝑘𝑙2
is l doubled is 2𝑙. So 𝑉 = 𝑘 2𝑙 2 = 4𝑘𝑙2 .
The length of a baby is directly proportional to its
weight. An average baby measures 50cm and has a
weight of 2.5kg. Estimate the weight of a baby
measuring 48cm long.
𝑙 = 20𝑤
𝑙𝛼𝑤
48 = 20𝑤
l = 𝑘𝑤
48
𝑤=
50 = 𝑘 × 2.5
20
50
𝑤 = 2.4𝑘𝑔
𝑘=
= 20
2.5
So 𝑙 = 20𝑤
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