x is directly proportional to y - OCR - GCSE Maths - Question 9 - 2020 - Paper 6

Since y is directly proportional to z, we can express this as:

$y = k_2 z$

where $k_2$ is another constant. Given that when $y = 8$, $z = 1.6$, we can substitute these values to find $k_2$:

$8 = k_2 \cdot 1.6 \Rightarrow k_2 = \frac{8}{1.6} = 5$.

We can now express z in terms of x using the relationships established:

From the first relationship: $y = \frac{1}{6} x$

Substituting this into the second equation, we have:

$\frac{1}{6} x = 5 z$

Rearranging for z gives us:

$z = \frac{1}{5} \cdot \frac{1}{6} x = \frac{x}{30}.$