Answer:
Direct proportionality states that:
if [tex]y \propto x[/tex]
then;
[tex]y = kx[/tex] .....[1] where, k is the constant of proportionality.
As per the statement:
The graph shown a proportional relationship.
From the graph we have;
[tex](\frac{1}{4}, \frac{3}{8})[/tex]
⇒[tex]x = \frac{1}{4}[/tex] and [tex]y = \frac{3}{8}[/tex]
Substitute these values in [1] we have;
[tex]\frac{3}{8} = k \cdot \frac{1}{4}[/tex]
Multiply both sides by 4 we have;
[tex]\frac{3}{2} = k[/tex]
or
[tex]k = \frac{3}{2}[/tex]
Therefore, the constant of proportionality is, [tex]\frac{3}{2}[/tex] or 3: 2