Question

the graph shows a proportional relationship from y to x that passes through the points located at (2, 6) and (3, 9). what is the constant of proportionality for the relationship? what is the equation of the line?

Explanation:

Step1: Recall the formula for constant of proportionality

For a proportional relationship \( y = kx \), the constant of proportionality \( k \) is given by \( k=\frac{y}{x} \).
We can use either of the points \((2, 6)\) or \((3, 9)\) to find \( k \). Let's use the point \((2, 6)\).
So, \( k=\frac{y}{x}=\frac{6}{2} = 3\).
We can verify with the other point \((3, 9)\): \( k=\frac{9}{3}=3 \).

Step2: Find the equation of the line

Since the relationship is proportional, the equation of the line is of the form \( y = kx \).
We found that \( k = 3 \), so the equation is \( y=3x \).

Answer:

The constant of proportionality is \( 3 \) and the equation of the line is \( y = 3x \).