1. Direct Proportion Direct Proportion Direct Proportion Graphs
Direct Proportion formula and calculations
Other Direct Proportion formula
Inverse Direct Proportion

2. Direct Proportion Direct Proportion
Two quantities, (for example, number of cakes and total
cost) are said to be in DIRECT Proportion, if :
“ .. When you double the number of cakes
you double the cost.”
Example : The cost of 6 cakes is £4.20. find the cost
of 5 cakes.
Cakes Cost
Write down two quantities that are in direct proportion.
6  4.20
1  4.20 ÷ 6 = 0.70
5  0.70 x 5 = £3.50

3. What name do we give to this value
Direct Proportion
Direct Proportion
Example : On holiday I exchanged £30 for $45.
How many $ will I get for £50.
What name do we give to this value
Exchange rate
£ $
30  45
1  45 ÷ 30 = 1.5
50  1.5 x 50 = $75

4. Direct Proportion Direct Proportion
Example : To make scrambled eggs for 2 people
we need 2eggs, 4g butter and 40 ml of milk.
How much of each for
(a) 4 people (b) Just himself
(a) Simply multiple by 2 :
4 eggs, 8g butter, 80 ml of milk.
(b) Simply half original amounts:
1 eggs, 2g butter, 20 ml of milk.

5. Direct Proportion Direct Proportion Graphs
The table below shows the cost of packets of “Biscuits”.
We can construct a graph to represent this data.
What type of graph do we expect ?

6. Direct Proportion Graphs
Notice that the points lie on a straight line passing through the origin
Direct Proportion Graphs
This is true for any two quantities which are in Direct Proportion.
1-Oct-19
Created by Mr. Lafferty Maths Dept.

7. Direct Proportion KeyPoint Two quantities which are in
Direct Proportion Graphs
KeyPoint
Two quantities which are in
Direct Proportion
always lie on a straight line
passing through the origin.

8. Direct Proportion X 1 2 3 4 y 6 9 12 Direct Proportion Graphs
Example : Plot the points in the table below.
Are they in Direct Proportion? X 1 2 3 4 y 6 9 12
We plot the points (1,3) , (2,6) , (3,9) , (4,12)

9. Direct Proportion Direct Proportion Graphs y 12 Plotting the points
(1,3) , (2,6) , (3,9) , (4,12) 11 10 9 8 7
Since we have a straight line
passing through the origin
x and y are in
Direct Proportion. 6 5 4 3 2 1 x 1 2 3 4

10. Find the formula connecting
Direct Proportion
Direct Proportion Graphs y 12
Find the formula connecting
y and x. 11 10 9
Formula has the form : 8 7
y = kx 6 5
Gradient = 3 4
Formula is : y = 3x 3 2 1 x 1 2 3 4

11. Direct Proportion Important facts: Direct Proportion Graphs
Fill in table
Find gradient from graph
Write down formula using knowledge
from straight line chapter

12. Direct Proportion Direct Proportion Formula
Given that y is directly proportional to x,
and when y = 20, x = 4.
Find a formula connecting y and x
Since y is directly proportional to x
the formula is of the form
k is the gradient
y = kx
20 = k(4)
k = 20 ÷ 4 = 5
y = 5x

13. Direct Proportion Direct Proportion Formula
The number of dollars (d) varies directly as the
number of £’s (P). You get 3 dollars for £2.
Find a formula connecting d and P.
Since d is directly proportional to P
the formula is of the form
k is the gradient
d = kP
3 = k(2)
k = 3 ÷ 2 = 1.5
d = 1.5P

14. Direct Proportion Direct Proportion Formula
How much will I get for £20
d = 1.5P
d = 1.5 x 20 = 30 dollars

15. Direct Proportion Harder Direct Proportion Formula
Given that y is directly proportional to the square of x, and when y = 40, x = 2.
Find a formula connecting y and x when .
Since y is directly proportional to x squared
the formula is of the form y x
y = kx2
40 = k(2)2
k = 40 ÷ 4 = 10
y = 10x2

16. Direct Proportion Harder Direct Proportion Formula
Calculate y when x = 5
y = 10x2
y = 10(5)2 = 10 x 25 = 250 y x

17. Direct Proportion Harder Direct Proportion Formula
The cost (C) of producing a football magazine
varies as the square root of the number of
pages (P). Given 36 pages cost 45p to produce.
Find a formula connecting C and P.
Since C is directly proportional to “square root of” P
the formula is of the form y x
k = 48 ÷ 6 = 8

18. Direct Proportion Harder Direct Proportion Formula
How much will 100 pages cost. y x

19. Inverse Proportion X 1 2 4 8 y 80 40 20 10 Inverse Proportion
Inverse Proportion is when one quantity increases
and the other decreases. The two quantities are said
to be INVERSELY Proportional
or (INDIRECTLY Proportional) to each other.
Example : Fill in the following table given x and y
are inversely proportional. y x X 1 2 4 8 y 80 40 20 10

20. Inverse Proportion Inverse Proportion
Inverse Proportion is the when one quantity increases
and the other decreases. The two quantities are said
to be INVERSELY Proportional
or (INDIRECTLY Proportional) to each other.
Example : If it takes 3 men 8 hours to build a wall.
How long will it take 4 men. (Less time !!) y x
Men Hours
3  8
1  3 x 8 = 24 hours
4  24 ÷ 4 = 6 hours

21. Inverse Proportion Inverse Proportion
Example : It takes 10 men 12 months to build a house.
How long should it take 15 men.
Men Months
10  12
1  12 x 10 = 120 y x
15  120 ÷ 15 = 8 months

22. Inverse Proportion Inverse Proportion
Example : At 8 m/s a journey takes 32 minutes.
How long should it take at 10 m/s.
Speed Time
8  32 mins
1  32 x 8 = 256 mins y x
10  256 ÷ 10 = 25.6 mins