Two points on a graph are (0, 0)

To find the constant of proportionality between the two points \((0, 0)\) and \((4, 1)\), we can use the formula for the constant of proportionality \(k\) in the context of a linear relationship defined by \(y = kx\).

We can find \(k\) using the coordinates of the second point \((4, 1)\):

\[ k = \frac{y}{x} = \frac{1}{4} \]

So, the constant of proportionality is \(\frac{1}{4}\).

Therefore, the answer is:

negative Start Fraction 1 over 4 End Fraction