Question

does this graph show a proportional relationship?

Explanation:

Step1: Recall Proportional Relationship

A proportional relationship is a linear relationship that passes through the origin \((0,0)\) and has a constant ratio \(\frac{y}{x}\) (slope) for all points.

Step2: Analyze the Graph

The given graph is a straight line (linear) and it passes through the origin \((0,0)\). To confirm the constant ratio, we can check points. For example, when \(x = 4\), \(y = 4\) (ratio \(\frac{4}{4}=1\)); when \(x = 10\), \(y = 10\) (ratio \(\frac{10}{10}=1\)). The slope is constant and it passes through the origin.

Answer:

Yes (The graph shows a proportional relationship because it is a straight line passing through the origin \((0,0)\) and the ratio \(\frac{y}{x}\) is constant for all points on the line.)