1. The problem asks to find the ratio of the change in $x$ to the change in $y$ between two points on a line. 2. From the graph, the two points are approximately $(2,1)$ and $(4,6)$. 3. Calculate the change in $x$: $$\Delta x = 4 - 2 = 2$$ 4. Calculate the change in $y$: $$\Delta y = 6 - 1 = 5$$ 5. The ratio of the change in $x$ to the change in $y$ is $$1 : n = \frac{\Delta x}{\Delta y} = \frac{2}{5}$$ 6. To express this ratio in the form $1 : n$, divide numerator and denominator by $2$: $$1 : \frac{5}{2}$$ 7. Therefore, the ratio is $1 : 2.5$. This means for every 1 unit change in $x$, there is a 2.5 unit change in $y$.