Ratio, proportion and rates of changeKey Stage 3

Recognising inverse proportion from a graph

Recognise the graph of inverse proportion.

  • In inverse proportion, is constant.
  • Use , where is a constant.
  • For positive values, the inverse-proportion curve approaches both axes. A decreasing graph alone is not enough.

Example 1

Does this graph show inverse proportion? Give a reason.

Check two points
The product is the same at every plotted point.
Yes

The plotted points have the same product . The curve has the form .

Example 2

Does this graph show inverse proportion? Give a reason.

Apply this to both sides.The products differ.
No

A decreasing straight line does not represent . Its products are not constant.

Your turn

Question 1

Does this graph show inverse proportion? Give a reason.

Check answer
Check two points
The product is the same at every plotted point.
Yes

The plotted points have the same product . The curve has the form .

Question 2

Does this graph show inverse proportion? Give a reason.

Check answer
Apply this to both sides.The products differ.
No

A decreasing straight line does not represent . Its products are not constant.

Question 3

Does this graph show inverse proportion? Give a reason.

Check answer
Check two points
The product is the same at every plotted point.
Yes

The plotted points have the same product . The curve has the form .

Question 4

Does this graph show inverse proportion? Give a reason.

Check answer
Apply this to both sides.The products differ.
No

A decreasing straight line does not represent . Its products are not constant.

Question 5

Does this graph show inverse proportion? Give a reason.

Check answer
Check two points
The product is the same at every plotted point.
Yes

The plotted points have the same product . The curve has the form .

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