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 $(0,0)$, and follows $y=kx$ where $k$ is a constant positive/negative value.

Step2: Analyze first graph

The line passes through $(0,0)$, and for points like $(2,4)$, $k=\frac{4}{2}=2$; $(5,10)$, $k=\frac{10}{5}=2$. It is a straight line through the origin, so it is proportional.

Step3: Analyze second graph

The line passes through $(0,0)$, and for points like $(4,1)$, $k=\frac{1}{4}=0.25$; $(10,3)$, $k=\frac{3}{10}=0.3$. Wait, correction: check consistency. Actually, it is a straight line through the origin, so $y=kx$ holds with constant $k$. For $(0,0)$, $(10,3)$, $k=0.3$, and $(5,1.5)$ would fit. It is a straight line through the origin, so it is proportional.

Answer:

Both the left graph (passing through (0,0) with slope 2) and the right graph (passing through (0,0) with slope 0.3) show a proportional relationship between x and y.