direct proportion direct proportion graphs direct proportion formula and calculations inverse direct...
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Direct Direct ProportionProportion
Direct Proportion Graphs
Direct Proportion formula and calculations
Inverse Direct Proportion
Direct Proportion
Other Direct Proportion formula
Direct Direct ProportionProportion
“ .. When you double the number of cakes you double the cost.”
Cakes Cost
Two quantities, (for example, number of cakes and totalcost) are said to be in DIRECT Proportion, if :
Direct Proportion
Example : The cost of 6 cakes is £4.20. find the cost of 5 cakes.
6 4.20 1 4.20 ÷ 6 = 0.70 5 0.70 x 5 = £3.50
Write down two quantities that
are in direct proportion.
Direct Direct ProportionProportion
£ $
Direct Proportion
Example : On holiday I exchanged £30 for $45.How many $ will I get for £50.
30 45 1 45 ÷ 30 = 1.5 50 1.5 x 50 = $75
What name do we give to
this value
Exchange rate
Direct Direct ProportionProportion
(a) Simply multiple by 2 :
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
4 eggs, 8g butter, 80 ml of milk.
(b) Simply half original amounts:
1 eggs, 2g butter, 20 ml of milk.
Direct Direct ProportionProportion
The table below shows the cost of packets of “Biscuits”.
Direct Proportion Graphs
No. of Pkts 1 2 3 4 5 6
Cost (p) 20 40 60 80 100 120
We can construct a graph to represent this data.
What type of graph do we expect ?
Apr 19, 2023Apr 19, 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Direct Proportion
0
20
40
60
80
100
120
140
0 1 2 3 4 5 6
No. of Packets
Cos
t (p
)
Direct Proportion GraphsNotice that the points lie on a straight line
passing through the origin
This is true for any two quantities
which are in Direct Proportion.
Direct Direct ProportionProportion
Direct Proportion Graphs
KeyPoint
Two quantities which are in Direct Proportion
always lie on a straight linepassing through the origin.
Direct Direct ProportionProportion
Example : Plot the points in the table below. Are they in Direct Proportion?
Direct Proportion Graphs
We plot the points (1,3) , (2,6) , (3,9) , (4,12)
XX 11 22 33 44
yy 33 66 99 1212
1
Direct Direct ProportionProportion
Plotting the points
(1,3) , (2,6) , (3,9) , (4,12)
Direct Proportion Graphs
0 1 2 3 4
101112
23456789
Since we have a straight linepassing through the origin
x and y are in Direct Proportion.
x
y
1
Direct Direct ProportionProportion
Find the formula connectingy and x.
Direct Proportion Graphs
0 1 2 3 4
101112
23456789
Formula has the form :
x
y
Gradient = 3
Formula is :y = 3x
y = kx
Direct Direct ProportionProportion
Direct Proportion Graphs
Important facts:Fill in table
Find gradient from graph
Write down formula using knowledge from straight line chapter
Direct Direct ProportionProportion
Q. Given that y is directly proportional to x, and when y = 20, x = 4.
Find a formula connecting y and x
Direct Proportion Formula
Since y is directly proportional to x the formula is of the form
y = kx k is the gradien
t20 = k(4)
k = 20 ÷ 4 = 5y = 5x
Direct Direct ProportionProportion
Q. 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.
Direct Proportion Formula
Since d is directly proportional to P the formula is of the form
d = kP k is the gradien
t3 = k(2)
k = 3 ÷ 2 = 1.5d = 1.5P
Direct Direct ProportionProportion
Q. How much will I get for £20
Direct Proportion Formula
d = 1.5P
d = 1.5 x 20 = 30 dollars
Direct Direct ProportionProportion
Q. 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 squaredthe formula is of the form
y = kx2
40 = k(2)2
k = 40 ÷ 4 = 10y = 10x2
Harder Direct Proportion Formula
y
x
Direct Direct ProportionProportion
Q. Calculate y when x = 5
y = 10x2
y = 10(5)2 = 10 x 25 = 250
Harder Direct Proportion Formula
y
x
Direct Direct ProportionProportion
Q. 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
k = 48 ÷ 6 = 8
Harder Direct Proportion Formula
C =k P48 =k 36
C =8 P
y
x
Direct Direct ProportionProportion
Q. How much will 100 pages cost.
Harder Direct Proportion Formula
C =8 100
C =8 100 =8×10 =80p
y
x
Inverse Inverse ProportionProportion
Inverse Proportion is when one quantity increasesand 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 yare inversely proportional.
Inverse Proportion
XX 11 22 44 88
yy 8080 102040
y
x
Inverse Inverse ProportionProportion
Men Hours
Inverse Proportion is the when one quantity increasesand 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 !!)
3 8 1 3 x 8 = 24 hours
4 24 ÷ 4 = 6 hours
Inverse Proportion
y
x
Inverse Inverse ProportionProportion
Men Months
Example : It takes 10 men 12 months to build a house.How long should it take 15 men.
10 12 1 12 x 10 = 120
15 120 ÷ 15 = 8 months
Inverse Proportion
y
x
Inverse Inverse ProportionProportion
Speed Time
Example : At 8 m/s a journey takes 32 minutes.How long should it take at 10 m/s.
8 32 mins 1 32 x 8 = 256 mins
10 256 ÷ 10 = 25.6 mins
Inverse Proportion
y
x