# Direct Proportion

...

Teacher recommended

- Created by: gogos
- Created on: 23-06-10 11:43

## Slides in this set

### Slide 1

Whiteboardmaths.com

7 2

1 5

© 2004 All rights reserved…read more

### Slide 2

Direct Proportion

If two quantities increase at the same rate so

that if one is doubled so is the other, then the 8

quantities are said to be directly proportional.

In the example shown, if C is the cost of an 7

ice cream and N is the number bought, we

6

write C N (C is proportional to N).

If two quantities are directly proportional 5

then their points lie on a straight line from Cost (£)

the origin. In our example the equation of 4

this line is C = kN for some value of k. k is Three ice creams

called the constant of proportionality and cost three times as

3 much as one etc.

has a value of 1.5 here.

2 Two ice creams cost

Eddie's Ices twice as much as one.

All £1.50 1

1 2 3 4 5

Number of Ice Creams…read more

### Slide 3

Direct Proportion

Terminology

y varies as x yx y varies directly as x

All mean the

y is proportional to x same thing

Strategy for solving proportion problems

1. Find the value of k (the constant of proportionality).

2. Use k together with given values to answer the question.

Example Question 1:

If y is proportional to z and y = 7 when z = 2, find:

(a) the value of y when z = 8

(b) the value of z when y = 10.5

yz (a) y = 3.5 x 8 = 28

y = kz (b) z = y/3.5 = 10.5/3.5 = 3

k = y/z

k = 7/2 = 3.5

y = 3.5z…read more

### Slide 4

Question 1:

If p is proportional to q and p = 3 when q = 12, find:

(a) the value of p when q = 30

(b) the value of q when p = 18

pq

p = kq

(a) p = 0.25 x 30 = 7.5

k = p/q

(b) q = p/0.25 = 18/0.25 = 72

k = 3/12

k = 0.25

p = 0.25q…read more

### Slide 5

Example Question 2

Given that y varies as x, fill in the missing values in the table below

x

3 5 10 20 70

y 7.5 12.5 50 175

25

From the table k = 25/10 = 2.5. All x values need to be multiplied by 2.5.

Question 2

Given that y varies as x, fill in the missing values in the table below

x 2 5 10 30 40

y 1.5 3.75 7.5 22.5 30

From the table k = 22.5/30 = 0.75. All x values need to be multiplied by 0.75.…read more

### Slide 6

Example Question 3

The Current I in a wire is proportional to the voltage V. If

I =12 amps when V = 8 volts find:

(a) The current when the voltage is 15 volts.

(b) The voltage when the current is 7.5 amps.

_

IV

I = kV

+

k = I/V

(a) I = 1.5 x 15 = 22.5 amps

k = 12/8

(b) V = I/1.5 = 7.5/1.5 = 5 volts

k = 1.5

I = 1.5V…read more

### Slide 7

### Slide 8

### Slide 9

### Slide 10

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## Similar Mathematics resources:

# Direct Proportion

...

Teacher recommended

- Created by: gogos
- Created on: 23-06-10 11:43

## Slides in this set

### Slide 1

Whiteboardmaths.com

7 2

1 5

© 2004 All rights reserved…read more

### Slide 2

Direct Proportion

If two quantities increase at the same rate so

that if one is doubled so is the other, then the 8

quantities are said to be directly proportional.

In the example shown, if C is the cost of an 7

ice cream and N is the number bought, we

6

write C N (C is proportional to N).

If two quantities are directly proportional 5

then their points lie on a straight line from Cost (£)

the origin. In our example the equation of 4

this line is C = kN for some value of k. k is Three ice creams

called the constant of proportionality and cost three times as

3 much as one etc.

has a value of 1.5 here.

2 Two ice creams cost

Eddie's Ices twice as much as one.

All £1.50 1

1 2 3 4 5

Number of Ice Creams…read more

### Slide 3

Direct Proportion

Terminology

y varies as x yx y varies directly as x

All mean the

y is proportional to x same thing

Strategy for solving proportion problems

1. Find the value of k (the constant of proportionality).

2. Use k together with given values to answer the question.

Example Question 1:

If y is proportional to z and y = 7 when z = 2, find:

(a) the value of y when z = 8

(b) the value of z when y = 10.5

yz (a) y = 3.5 x 8 = 28

y = kz (b) z = y/3.5 = 10.5/3.5 = 3

k = y/z

k = 7/2 = 3.5

y = 3.5z…read more

### Slide 4

Question 1:

If p is proportional to q and p = 3 when q = 12, find:

(a) the value of p when q = 30

(b) the value of q when p = 18

pq

p = kq

(a) p = 0.25 x 30 = 7.5

k = p/q

(b) q = p/0.25 = 18/0.25 = 72

k = 3/12

k = 0.25

p = 0.25q…read more

### Slide 5

Example Question 2

Given that y varies as x, fill in the missing values in the table below

x

3 5 10 20 70

y 7.5 12.5 50 175

25

From the table k = 25/10 = 2.5. All x values need to be multiplied by 2.5.

Question 2

Given that y varies as x, fill in the missing values in the table below

x 2 5 10 30 40

y 1.5 3.75 7.5 22.5 30

From the table k = 22.5/30 = 0.75. All x values need to be multiplied by 0.75.…read more

### Slide 6

Example Question 3

The Current I in a wire is proportional to the voltage V. If

I =12 amps when V = 8 volts find:

(a) The current when the voltage is 15 volts.

(b) The voltage when the current is 7.5 amps.

_

IV

I = kV

+

k = I/V

(a) I = 1.5 x 15 = 22.5 amps

k = 12/8

(b) V = I/1.5 = 7.5/1.5 = 5 volts

k = 1.5

I = 1.5V…read more

### Slide 7

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### Slide 9

### Slide 10

## Comments

## Similar Mathematics resources:

## Related discussions on The Student Room

- Direct and Inverse proportion question »
- Direct/Inverse Proportion »
- how do u do direct and indirect proportion »
- maths gcse edexcel higher paper 2 »
- Sports Direct »
- Definition of Significant Proportion under The UK Gambling ... »
- Schools direct salaried salary »
- Police direct entry to detective »
- Number of Christians (and Muslims) to grow, proportion of ... »
- Can someone give my economics essay a mark out of 25? »

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