1. Direct Proportion
Objective- To be able to write equations that link variables which are directly proportional

2. Direct proportion
If two variables are directly proportional that means that if one doubles the other doubles
If one is multiplied by ten, the other is multiplied by ten
If one if halved the other is halved
The two variables are linked by a constant (k)

3. General equation A is directly proportional to B so,
A∞ B .The general equation is A=kB where k is a constant
that is A/B = K
X is directly proportional to Y so,
X∞ Y
The general equation is X=kY where k is a constant.
X/Y = K

4. General equation practise
Write out the general equation for each statement:
A is directly proportional to B
A is directly proportional to the square of B
A is directly proportional to the square root of B
A is directly proportional to the cube of B
Answers
A=kB
A=kB2
A=k “square root” B
A=kB3
Note- Don’t write “square root” when you mean square root, use the square root symbol!

5. Finding K
In the question you will be given a pair of values to help you find k for example:
A and B are directly proportional when A=6 B=2
So A/B = K
6÷2=k
3=k

6. Example 1
A is directly proportional to B. When A=20 B=5 write an equation linking A and B
A/B = K
20÷5=k
4=k
The final equation is A=4B

7. Example 2
A is directly proportional to the square of B. When A=40 B=2 write an equation linking A and B
A=Kb2
40=k x 22
40÷ 22 =k
10=k
The final equation is A=10B2

8. Example 3
A is directly proportional to the cube of B. When A=250 B=5 write an equation linking A and B
A/B3 = K
250÷ 53 =k
2=k
The final equation is A=2B3

9. Questions
A is directly proportional to B. When A=18, B=3. Write an equation linking A and B
A is directly proportional to B. When A=42, B=10. Write an equation linking A and B
A is directly proportional to B2. When A=45, B=3. Write an equation linking A and B
A is directly proportional to B2. When A=5, B=5. Write an equation linking A and B
A is directly proportional to the square root of B. When A=18, B=4. Write an equation linking A and B
A is directly proportional to the square root of B. When A=35, B=100. Write an equation linking A and B
A is directly proportional to the cube of B. When A=54, B=3. Write an equation linking A and B
A is directly proportional to the cube of B. When A=500, B=5. Write an equation linking A and B

10. Answers A=6B A=4. 2B A=5B2 A=0.2B2 A= 9rootB A=3.5rootB A=2B3 A=4B3
Note- Don’t write “root” when you mean square root, use the square root symbol!