Direct and Inverse Direct and Inverse ProportionProportion

Direct and Inverse Direct and Inverse ProportionProportion

Chapter 2

(Book 2)

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Direct Direct

ProportionProportion

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Direct Proportion

Two quantities are directly proportional if an increase in one quantity corresponds to a constant increase in the other quantity, or if a decrease in one quantity corresponds to a constant decrease in the other quantity.

X Y X Y

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Example:

“Jim’s wages are directly proportional to the hours he works”

The more hours he works, the more money he earns.

This could be written as:

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HoursWages Or...

Wages = k x Hours

k is the “constant of proportionality”

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Direct Proportion GraphsDirect Proportion Graphs

The table below shows the “cost of packets of Biscuits”which is directly proportional to the “no. of packets.”

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 ?

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Points to remember for graph:Points to remember for graph:

For the data given in the previous slide C∝ N

1. For the above relation N is the independent variable and C is the dependent variable.

2. On the graph we always take the independent variable on the X axis and the dependant variable on the Y axis.

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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.

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Direct Proportion GraphDirect Proportion Graph

KeyPoint

Two quantities which are in Direct Proportion

always lie on a straight linepassing through the origin.

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Direct Proportion GraphsDirect Proportion Graphs

Example : Plot the points in the table below. Are they in Direct Proportion?

We plot the points (1,3) , (2,6) , (3,9) , (4,12)

XX 11 22 33 44

yy 33 66 99 1212

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Direct Proportion GraphsDirect Proportion Graphs

1

Plotting the points

(1,3) , (2,6) , (3,9) , (4,12)

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

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Inverse ProportionInverse Proportion

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Inverse Proportion

Two quantities are inversely proportional if an increase in one quantity corresponds to a constant decrease in the other quantity, or if a decrease in one quantity corresponds to a constant increase in the other quantity.

X YYX

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Inverse ProportionInverse Proportion

Example:

“It takes 4 men 10 days to build a brick wall. How many days will it take 20 men?”

The more men employed, the less time it takes to build the wall

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Time is inverselyProportional to Men

t ∝ m

1

15

t = m

k4

10k

40104 k

t = m

40If we have 20 men, m = 20

t = 20

40= 2 days

(The first step is to calculate the value of K and form the equation using the known values)

(The second step is to use the equation with the value of K to calculate unknown values)

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Try this when:Try this when:

M is inversely proportional to RIf M = 9 when R = 4a. Find M when R =2b. Find R when M = 3

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Indirect Proportion GraphsIndirect Proportion Graphs

The table below shows the “number of days to make a house” which is indirectly proportional to the “number of men.”

We can construct a graph to represent this data.

What type of graph do we expect ?

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Men (M) 5 10 15 20 25 30

Days (D) 300 150 100 75 60 50

Points to remember for graph:Points to remember for graph:

For the data given in the previous slide M∝ 1/D

1. For the above relation M is the independent variable and D is the dependent variable.

2. On the graph we always take the independent variable on the X axis and the dependant variable on the Y axis.

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Indirect Proportion Graphs

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Notice that the points lie on a

curved line

This is true for any two quantities which are in

Indirect Proportion.

Indirect Proportion GraphIndirect Proportion Graph

KeyPoint

Two quantities which are Indirectly Proportion

always make a curved graph.

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Best of Luck!Best of Luck!

If you have any further queries regarding the topic

or have any problems don’t hesitate to ask.

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