Finding the constant of proportionality for direct proportion | Maths

Starter quiz

Any non-zero number multiplied by its ______ is equal to 1.

additive inverse

reciprocal ✓

difference
Which of the following tables show direct proportion?

a ✓

b ✓

c

d ✓
Match the numbers to their reciprocals.

$1\over8$

⇔

8 ✓

$8\over3$

⇔

$3\over8$ ✓

$1\over3$

⇔

3 ✓

6

⇔

$1\over6$ ✓

$6\over5$

⇔

$5\over6$ ✓
Decide which of the following would share a directly proportional relationship.

The time taken to make 10 000 items and the number of machines

The height of a staircase and the number of stairs ✓

The cost to wallpaper a room and the size of the room ✓

The number of sweets in a bag and the number of people sharing it
$h$ is directly proportional to $g$ . When $g$ = 17, $h$ = 93.5. Find $h$ when $g$ = 25.

'137.5' ✓
$h$ is directly proportional to $g$ . When $h$ = 17, $g$ = 93.5. Find $g$ when $h$ = 60.5.

'11' ✓

Exit quiz

When dealing with equations of direct proportion we use the equation $y = kx$ . What does $k$ represent?

the additive relationship between $x$ and $y$

the difference between $x$ and $y$

the constant of proportionality ✓
Which of the following equations represent $y$ being directly proportional to some form of $x$ ?

$y=3x$ ✓

$y=\sqrt{3}x$ ✓

$y=3x+1$

$y=3\sqrt{x}$

$y={x\over3}$ ✓
Match each equation to its correct value of $k$ .

$y={x\over6}$

⇔

$1\over6$ ✓

$y={\sqrt6{x}}$

⇔

${\sqrt6}$ ✓

$y={5x\over6}$

⇔

$5\over6$ ✓

$y={\sqrt5{x}}$

⇔

${\sqrt5}$ ✓

$y={6x\over5}$

⇔

$6\over5$ ✓
$y$ is directly proportional to $x$ . When $x$ = 13, $y$ = 52. Write an equation connecting $x$ and $y$ .

$y=x+4$

$y=4x$ ✓

$y=x-4$

$y=4x+4$
$y$ is directly proportional to $x$ . When $x$ = 6, $y$ = 13.2. Write an equation connecting $x$ and $y$ and use this to find the value of $y$ when $x$ = 14.

'30.8' ✓
$y$ is directly proportional to $x$ . When $x$ = 6, $y$ = 13.2. Write an equation connecting $x$ and $y$ and use this to find the value of $x$ when $y$ = 123.2.

'56' ✓

Worksheet

Loading worksheet ...

Presentation

Loading presentation ...

Video

Lesson Details

Key learning points

Direct proportion equations are of the form y = kx
k is the constant of proportionality and it is also the gradient of the graph.
To find the gradient, k, you can use two sets of coordinates (pairs of values).

Common misconception

Failing to recognise that x/2 is the same as 1/2 × x and therefore shows a directly proportional relationship where the value of k is 1/2.

It is useful to go back to looking at unit fractions. E.g. 2/3 = 1/3 × 2 and 7/9 = 1/9 × 7, etc. And, then look at algebraic terms leading up to for example, 2x/3. 'What is the the multiplier?'

Keywords

Direct proportion - Two variables are in direct proportion if they have a constant multiplicative relationship