Question

Select the tables that show a proportional relationship between x and y.

X 4 8 12
Y 3 6 9

X 4 8 12
Y 5 10 15

Answer 1

To determine if there is a proportional relationship between \( x \) and \( y \) in each table, we can check whether the ratios \( \frac{y}{x} \) are constant.

1. For the first table:

\[
\begin{align*}
\text{When } x = 4, & \quad y = 3 \quad \Rightarrow \quad \frac{y}{x} = \frac{3}{4} = 0.75 \\
\text{When } x = 8, & \quad y = 6 \quad \Rightarrow \quad \frac{y}{x} = \frac{6}{8} = \frac{3}{4} = 0.75 \\
\text{When } x = 12, & \quad y = 9 \quad \Rightarrow \quad \frac{y}{x} = \frac{9}{12} = \frac{3}{4} = 0.75 \\
\end{align*}
\]

The ratio \( \frac{y}{x} \) is constant at \( 0.75 \), indicating a proportional relationship.

2. For the second table:

\[
\begin{align*}
\text{When } x = 4, & \quad y = 5 \quad \Rightarrow \quad \frac{y}{x} = \frac{5}{4} = 1.25 \\
\text{When } x = 8, & \quad y = 10 \quad \Rightarrow \quad \frac{y}{x} = \frac{10}{8} = 1.25 \\
\text{When } x = 12, & \quad y = 15 \quad \Rightarrow \quad \frac{y}{x} = \frac{15}{12} = 1.25 \\
\end{align*}
\]

The ratio \( \frac{y}{x} \) is also constant at \( 1.25 \), indicating a proportional relationship.

Both tables show a proportional relationship between \( x \) and \( y \).