Question

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 \( x
eq0 \)).

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