Direct and inverse proportion Worked Solutions — GCSE Maths

Identify the type of proportion

Directly proportional means $y = kx$: multiply $x$ by a number and $y$ is multiplied by the same number.

Write the general formula

Here $k$ is the constant of proportionality. It is the same for every pair of values in the relationship.

Divide y by x to find k

For direct proportion $k = \frac{y}{x}$, so $k = 20 \div 4 = 5$.

Identify the type of proportion

Directly proportional means $y = kx$: multiply $x$ by a number and $y$ is multiplied by the same number.

Find the constant of proportionality

Divide $y$ by $x$: $k = 5$, so $y = 5x$.

Substitute $x = 7$

So $y = 35$ when $x = 7$.

Identify the type of proportion

Inversely proportional means $y = \frac{k}{x}$: multiply $x$ by a number and $y$ is divided by that number.

Write the general formula

Here $k$ is the constant of proportionality. For inverse proportion the product $x \times y$ is always the same.

Multiply x by y to find k

For inverse proportion $k = xy$, so $k = 30$.

Identify the type of proportion

Inversely proportional means $y = \frac{k}{x}$: multiply $x$ by a number and $y$ is divided by that number.

Find the constant of proportionality

The product $xy$ is constant, so $k = 36$ and $y = \frac{36}{x}$.

Substitute $x = 6$

So $y = 6$ when $x = 6$.

Write down what direct proportion means

Direct proportion always has the form $y = kx$.

Find the value of y when x is zero

The graph must pass through the origin $(0, 0)$.

Describe the shape

A constant gradient $k$ gives a straight line, and it goes through the origin.