Question

select the graphs that show a proportional relationship between x and y.

Explanation:

Step1: Recall Proportional Relationship

A proportional relationship between \(x\) and \(y\) is of the form \(y = kx\) (where \(k\) is a constant), and its graph is a straight line passing through the origin \((0,0)\).

Step2: Analyze First Graph

The first graph (left) has a line that starts at \((0,0)\) (the origin) and goes up, so it passes through the origin. This fits the form \(y = kx\).

Step3: Analyze Second Graph

The second graph (right) has a line that starts at \((0,4)\), not the origin. So it's of the form \(y = kx + b\) with \(b = 4\), which is a linear but not proportional relationship.

Answer:

The graph on the Left