Proportion modelled algebraically | Maths | Quizalize & Oak National Academy

Starter quiz

Which of the following equations of a line show the direct proportion between $x$ and $y$ ?

$y = 3x + 10$

$y = 3x$ ✓

$y = 5x - 2$

$y = 5x$ ✓
Which of the following equations of a curve show the direct proportion between $x^2$ and $y$ ?

$y=4x^2$ ✓

$y=(x-3)(x-4)$

$y=x(x-10)$

$y=2x^2$ ✓
Which of the following show that $x$ is inversely proportional to $y$ ?

$y=\frac{3}{x}$ ✓

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

$y=\frac{3}{5x}$ ✓

$y=\frac{5x}{3}$
Given that $y$ is directly proportional to $𝑥$ and $𝑦=30$ when $x=5$ , write the equation connecting $y$ and $x$ .

'y=6x' ✓
Given that $y$ is directly proportional to $𝑥^2$ and $𝑦=4375$ when $x=25$ , write the equation connecting $y$ and $x^2$ .

$y=875x$

$y=7x^2$ ✓

$y=175x$

$y=49x^2$
Given that $y\propto \frac{1}{𝑥}$ and $𝑦=4$ when $x=50$ , write the equation connecting $y$ and $x$ .

$y=\frac{400}{𝑥}$

$y=\frac{x}{400}$

$y=\frac{200}{x}$ ✓

$y=\frac{x}{200}$

Exit quiz

Which of the following show an inversely proportional relationship between $y$ and $x^n$ ?

$y=\frac{4}{x^2}$ ✓

$y=\frac{3}{4x}$ ✓

$y=\frac{3x}{4}$

$y=\frac{x^2}{4}$
Which of these graphs show direct proportion between $y$ and $x^n$ ?

C, D, E ✓

A, B, C, D, E

A, C, D, E, F

All

None
Match the graph with the equation.

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

⇔

A ✓

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

⇔

B ✓

$y=kx$

⇔

C ✓

$y=k\sqrt{x}$

⇔

D ✓

$y=kx^2$

⇔

E ✓

$y=kx+c$

⇔

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

'multiplicative' ✓
$Match the value of <Math>k</Math> with the relevant graph for <Math>y=\frac{k}{x}</Math>$

Match the value of $k$ with the relevant graph for $y=\frac{k}{x}$

$k=20$

⇔

A ✓

$k=2$

⇔

C ✓

$k=10$

⇔

B ✓
$Match the value of <Math>k</Math> with the relevant graph for <Math>y=\frac{k}{x^2}</Math>$

Match the value of $k$ with the relevant graph for $y=\frac{k}{x^2}$

$k=20$

⇔

A ✓

$k=2$

⇔

C ✓

$k=10$

⇔

B ✓

Worksheet

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Lesson Details

Key learning points

The question does not always state the type of proportion.
The context of the question can be used to determine the type of proportion.
If more than one pair of values is given, this can determine the type of proportion.

Common misconception

The constant of proportionality shows the gradient for inversely proportional graphs.

The constant of proportionality shows the gradient for directly proportional graphs only. The constant for a reciprocal graph in the form k/x^n, shows the distance of the reciprocal from the origin.

Keywords

Inversely proportional - Two variables are inversely proportional if there is a constant multiplicative relationship between one variable and the reciprocal of the other.
Direct proportion - Two variables are in direct proportion if they have a constant multiplicative relationship.