Finding the constant of proportionality for inverse proportion | Maths

Starter quiz

Match the statement with the correct notation.

$y\propto x$

⇔

$y$ is proportional to $x$ ✓

$y\propto x^2$

⇔

$y$ is proportional to $x^2$ ✓

$y \propto \frac{1}{x^2}$

⇔

$y$ is inversely proportional to $x^2$ ✓

$y \propto \frac{1}{x}$

⇔

$y$ is inversely proportional to $x$ ✓
Match the coordinates with the directly proportional equations.

(4,12)

⇔

$y=3x$ ✓

(9,3)

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$y=\frac {x}{3}$ ✓

(6,8)

⇔

$y=\frac {4x}{3}$ ✓

(10,2)

⇔

$y=\frac {x}{5}$ ✓

(2,10)

⇔

$y=5x$ ✓
$y$ is proportional to $x$ . When $y$ = 48, $x$ = 12. What is the equation to show the direct proportion between $x$ and $y$ ?

$y=2x$

$y=\frac{4}{x}$

$y=4x$ ✓

$y=\frac{2}{x}$
$y$ is proportional to $x$ . When $y$ = 20, $x$ = 80. What is the equation to show the direct proportion between $x$ and $y$ ?

$y=\frac{1}{4x}$

$y=\frac{0.25}{x}$

$y=\frac{4}{x}$

$y=\frac{x}{4}$ ✓
$y$ is proportional to $x^2$ . When $y$ = 200, $x$ = 10. What is the equation to show the direct proportion between $x$ and $y$ ?

$y=2x$

$y=(2x)^2$

$y=2x^2$ ✓

$y=\frac{x^2}{2}$
$y$ is proportional to $\sqrt{x}$ . When $y$ = 2, $x$ = 36. What is the equation to show the direct proportion between $x$ and $y$ ?

$y=\frac{1}{\sqrt{x}}$

$y=\frac{4}{\sqrt{x}}$

$y=\frac{\sqrt{x}}{3}$ ✓

$y=\frac{3}{\sqrt{x}}$

Exit quiz

Match the constant of proportionality for each of the following inverse proportions.

$y=\frac{2}{x}$

⇔

2 ✓

$y=\frac{1}{2x}$

⇔

$\frac{1}{2}$ ✓

$y=\frac{3}{2x}$

⇔

1.5 ✓

$y=\frac{2}{3x}$

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$\frac{2}{3}$ ✓
Match the correct proportionality statement with an example equation.

$y=4x$

⇔

$y$ is proportional to $x$ ✓

$y=4x^2$

⇔

$y$ is proportional to $x^2$ ✓

$y = \frac{4}{x^2}$

⇔

$y$ is inversely proportional to $x^2$ ✓

$y =\frac{4}{x}$

⇔

$y$ is inversely proportional to $x$ ✓
$y$ is $\propto \frac{1}{x}$ . When $y$ = 4, $x = 2$ . What is the equation to show the inversely proportional relationship between $x$ and $y$ ?

$y=8x$

$y=\frac{8}{3x}$

$y=\frac{x}{8}$

$y=\frac{8}{x}$ ✓

$y=\frac{24}{x}$
$y$ is $\propto \frac{1}{x}$ . When $y=\frac{1}{5}$ , $x=2$ . Work out $y$ when $x=10$ . Give your answer as a decimal.

'0.04' ✓
$y$ is $\propto \frac{1}{x^2}$ . When $y=\frac{1}{6}$ , $x=2$ . Work out $y$ when $x=\sqrt{8}$ .

12

$\frac{1}{12}$ ✓

$\frac{2}{3}$

$\frac{3}{2}$
$y$ is $\propto \frac{1}{\sqrt{x}}$ . When $y=2.4$ , $x=100$ . Work out $y$ when $x=64$ .

'3' ✓

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Lesson Details

Key learning points

Inverse proportion equations are of the form y = k ÷ x^n
The equation can be written in the form yx^n = k
k is the constant of proportionality.
To find k, you can use a pair of values.

Common misconception

For all direct and inverse proportions, the multiplicative relationship is with x and y.

The multiplicative relationship whether direct or inverse can be shown as y and x^n. Show a ratio table of y and 1/x^2 and a table of y and 1/x. The inverse multiplicative relationship is seen with y and 1/x^2 and not with 1/x.

Keywords

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