Question

Do the two tables show the same proportional relationship between x and​ y? Explain.
x
50
75
100
y
​1,250
​1,875
​2,500
x
3
4
5
y
4.2
5.6
7
Question content area bottom
Part 1
▼
each table shows
▼
proportional relationship. In the first​ table, every ratio StartFraction y Over x EndFraction
is equivalent to
  
enter your response here. In the second​ table, every ratio StartFraction y Over x EndFraction
is equivalent to
  
enter your response here.
​(Simplify your​ answers.)

Answer 1

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 \( 1.4 \).