what is the constant of proportionality?

Explanation:

Step1: Recall the formula for proportionality

For a proportional relationship ( y = kx ), the constant of proportionality ( k ) is ( \frac{y}{x} ) (where ( x\neq0 )).

Step2: Pick a point from the graph

Looking at the graph, when ( x = 1 ), let's find the corresponding ( y )-value. From the line, when ( x = 1 ), ( y = 6 ) (we can also check other points, like when ( x = 2 ), ( y = 12 ), etc.).

Step3: Calculate the constant of proportionality

Using the formula ( k=\frac{y}{x} ), substitute ( x = 1 ) and ( y = 6 ). So ( k=\frac{6}{1}=6 ). We can verify with another point: if ( x = 2 ), ( y = 12 ), then ( \frac{12}{2}=6 ), which confirms the constant.

Answer:

6