Question

Two points on a graph are (0, 0)
and (4, 1)
. Identify the constant of proportionality.

Answer 1

To find the constant of proportionality between the two points \((0, 0)\) and \((4, 1)\), we need to check if there is a linear relationship that can be expressed in the form \(y = kx\), where \(k\) is the constant of proportionality.

Starting with the two points:
1. The first point \((0, 0)\) represents the origin, which means when \(x = 0\), \(y\) also equals \(0\).
2. The second point is \((4, 1)\).

Using the point \((4, 1)\) to find the constant of proportionality \(k\):

\[
y = kx
\]
Substituting \(x = 4\) and \(y = 1\):

\[
1 = k(4)
\]

To solve for \(k\):

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

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