Question

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

Explanation:

Step1: Recall proportional graph rules

A proportional relationship graph is a straight line passing through the origin \((0,0)\), following \(y = kx\) where \(k\) is a constant.

Step2: Analyze first graph

The line starts at \((0,0)\) and is straight, fitting \(y = kx\) (here \(k = \frac{10}{8} = 1.25\)).

Step3: Analyze second graph

The line starts at \((0,4)\), not the origin. It follows \(y = kx + 4\), which is non-proportional.

Answer:

The left graph (the straight line passing through the origin) shows a proportional relationship between \(x\) and \(y\).