Bot GPT 4-o mini To determine whether the two tables show the same proportional relationship between \( x \) and \( y \), we need to calculate the ratios \( \frac{y}{x} \) for each value in both tables.
For the first table:
\[ \begin{align*} x = 50, & \quad y = 1,250 \quad \Rightarrow \quad \frac{y}{x} = \frac{1250}{50} = 25 \ x = 75, & \quad y = 1,875 \quad \Rightarrow \quad \frac{y}{x} = \frac{1875}{75} = 25 \ x = 100, & \quad y = 2,500 \quad \Rightarrow \quad \frac{y}{x} = \frac{2500}{100} = 25 \ \end{align*} \]
In the first table, every ratio \( \frac{y}{x} \) is equivalent to \( 25 \).
For the second table:
\[ \begin{align*} x = 3, & \quad y = 4.2 \quad \Rightarrow \quad \frac{y}{x} = \frac{4.2}{3} \approx 1.4 \ x = 4, & \quad y = 5.6 \quad \Rightarrow \quad \frac{y}{x} = \frac{5.6}{4} = 1.4 \ x = 5, & \quad y = 7 \quad \Rightarrow \quad \frac{y}{x} = \frac{7}{5} = 1.4 \ \end{align*} \]
In the second table, every ratio \( \frac{y}{x} \) is equivalent to \( 1.4 \).
Conclusion:
The two tables do not show the same proportional relationship between \( x \) and \( y \) because the ratios are different. In the first table, every ratio \( \frac{y}{x} \) is \( 25 \), while in the second table, every ratio \( \frac{y}{x} \) is \( 1.4 \).
To summarize the answers:
- In the first table, every ratio \( \frac{y}{x} \) is equivalent to \( 25 \).
- In the second table, every ratio \( \frac{y}{x} \) is equivalent to \( 1.4 \).
1 answer