1. The problem asks for the constant of proportionality $\frac{y}{x}$ for a line passing through the origin and the point $(1,40)$. 2. The constant of proportionality in a direct variation $y = kx$ is the ratio $\frac{y}{x} = k$. 3. Using the point $(1,40)$, substitute $x=1$ and $y=40$ into $k = \frac{y}{x}$: $$k = \frac{40}{1}$$ 4. Simplify the fraction: $$k = 40$$ 5. Therefore, the constant of proportionality is 40. This means for every increase of 1 in $x$, $y$ increases by 40.