Question

what is the constant of proportionality?

Explanation:

Step1: Recall the formula for constant of proportionality

For a proportional relationship \( y = kx \), the constant of proportionality \( k \) is given by \( k=\frac{y}{x} \), where \( (x,y) \) is a point on the line.

Step2: Choose a point on the line

Let's take the point \( (2, 200) \) (from the graph, when \( x = 2 \), \( y = 200 \)).

Step3: Calculate the constant of proportionality

Using the formula \( k=\frac{y}{x} \), substitute \( x = 2 \) and \( y = 200 \). So \( k=\frac{200}{2}=100 \). We can verify with another point, say \( (10, 1000) \), \( k=\frac{1000}{10}=100 \), which confirms the value.

Answer:

100