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.

Step2: Check first graph

The line starts at $(0,0)$, is straight, and $\frac{y}{x}$ is constant (e.g., at $x=10$, $y=3$, so $k=\frac{3}{10}=0.3$; at $x=5$, $y=1.5$, $\frac{1.5}{5}=0.3$).

Step3: Check second graph

The line starts at $(0,0)$, is straight, and $\frac{y}{x}$ is constant (e.g., at $x=4$, $y=10$, so $k=\frac{10}{4}=2.5$; at $x=2$, $y=5$, $\frac{5}{2}=2.5$).

Answer:

Both the left graph and the right graph show a proportional relationship between $x$ and $y$.