Foundation and Higher · direct and inverse proportion

Direct or inverse
proportion?
How to tell.

does it double,
or does it halve?

two quantities, linked —

Proportion

direct: one doubles, the other doubles

inverse: one doubles, the other halves

step 1 of 4

Direct: a table

1. Double the hours: double the pay.

2. Divide each pair: always £9 per hour.

✓ Direct: the ratio stays the same

pay ÷ hours is always 9

hours worked

2

4

6

10

pay

£18

£36

£54

£90

step 2 of 4

Direct: the graph

1. A straight line.

2. It must pass through the origin.

✓ Nothing worked, nothing paid: (0, 0)

step 3 of 4

Inverse: a table

1. Double the builders: half the time.

2. Multiply each pair: always 24.

✓ Inverse: the product stays the same

builders × days is always 24

number of builders

1

2

4

8

days taken

24

12

6

3

step 4 of 4

Inverse: the graph

1. A curve that falls, quickly at first.

2. It gets close to the axes, never touches.

✓ The reciprocal shape

direct or inverse —

Direct

y ÷ x is constant

Inverse

x × y is constant

Graphs

line through (0, 0), or a curve

Test it: double one.
What happens to the other?

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