Checking and securing understanding of inverse proportion graphs | Maths

Starter quiz

If two variables have a constant ______ relationship, they are in direct proportion.

additive

multiplicative ✓

decreasing
Which of the following tables show values of A and B in direct proportion?
Which of the following graphs show direct proportion?
Calculate the value of k (constant of proportionality).

$3\over5$

$1\over3$

$5\over3$ ✓

3
What is the equation of this line?

$y={3\over5}$

$y={5\over3}x$ ✓

$y={5\over3}$

$y={3\over5}x$
Which is the graph of $y={1\over3}x$ ?

A ✓

B

C

D

Exit quiz

Two variables are inversely proportional if there is a constant multiplicative relationship between one variable and the ______ of the other.

'reciprocal' ✓
Which of the following is an example of inverse proportion?

The number of euros exchanged and the number of pounds

The number of sweets and the number of bags of sweets

The number of kilometres travelled and the number of miles travelled

The time taken to build a wall and the number of people ✓

The cost to fill a fuel tank and the size of the tank
Which of the following is an equation representing inverse proportion?

$y={{{50}\over{x}}+5}$

$y={{{50}\over{x}}}$ ✓

$y={{{50}\over{x}}-5}$

$y={{{x}\over{50}}}$
Which of the following are not true? A graph representing inverse proportion...

will appear in all 4 quadrants. ✓

will not intersect the $x$ and $y$ axes.

will appear in only 2 quadrants.

will intersect the $x$ and $y$ axes. ✓
The ______ the dividend, the closer to the origin the graph will be.

'smaller' ✓
Which of the following is the graph of $y={{{2.5}\over{x}}}$ ?

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Lesson Details

Key learning points

Inverse proportion can be recognised graphically.
An inverse proportion graph is always a curve that does not touch either axis.
The equation is of the form y = k/x
k is the constant of proportionality.

Common misconception

Assuming the the graph will eventually intercept the axes.

Pupils can experiment with very large numbers. Here a spreadsheet is useful to generate numbers very quickly and show that although it gets very close to zero it never actually gets there.

Keywords

Inverse proportion - Two variables are inversely proportional if there is a constant multiplicative relationship between one variable and the reciprocal of the other