Question

determine if the graph represents a proportional relationship. show your work.

Explanation:

Step1: Recall proportional relationship rule

A proportional relationship has the form \( y = kx \), where \( k \) is the constant of proportionality, and the graph passes through \((0,0)\) with a constant ratio \(\frac{y}{x}\) for all points.

Step2: Calculate the ratio \(\frac{y}{x}\) for each point

• For \((1, 4)\): \(\frac{4}{1} = 4\)
• For \((2, 8)\): \(\frac{8}{2} = 4\)
• For \((-1, -4)\): \(\frac{-4}{-1} = 4\)
• For \((-2, -8)\): \(\frac{-8}{-2} = 4\)
• For \((0, 0)\): The ratio is undefined in the usual sense, but the graph passes through the origin.

Step3: Check if the ratio is constant

All non - zero \( x \) points have a ratio of \( y/x = 4 \), and the graph passes through \((0,0)\). So the relationship is proportional.

Answer:

The graph represents a proportional relationship.