Do the two tables show the same proportional relationship between x and​ y? Explain.

Question

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:

$$\begin{array}{rlrl}x=50,& y=1,250\Rightarrow \frac{y}{x}=\frac{1250}{50}=25x=75,& y=1,875\Rightarrow \frac{y}{x}=\frac{1875}{75}=25x=100,& y=2,500\Rightarrow \frac{y}{x}=\frac{2500}{100}=25\end{array}$$

In the first table, every ratio $\frac{y}{x}$ is equivalent to $25$.

For the second table:

$$\begin{array}{rlrl}x=3,& y=4.2\Rightarrow \frac{y}{x}=\frac{4.2}{3}\approx 1.4x=4,& y=5.6\Rightarrow \frac{y}{x}=\frac{5.6}{4}=1.4x=5,& y=7\Rightarrow \frac{y}{x}=\frac{7}{5}=1.4\end{array}$$

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 $1.4$.