Question

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

x 2 4 8
y 3 6 8

x 3 6 15
y 4 8 20

Answer 1

To determine if there is a proportional relationship between \( x \) and \( y \), we need to check if the ratio \( \frac{y}{x} \) is constant for each set of \( x \) and \( y \) values.

Let's analyze the first set of values:

**First set:**

\[
\begin{align*}
x & : 2, 4, 8 \\
y & : 3, 6, 8 \\
\end{align*}
\]

Calculating the ratios \( \frac{y}{x} \):

1. For \( x = 2 \), \( y = 3 \):
\[
\frac{y}{x} = \frac{3}{2} = 1.5
\]

2. For \( x = 4 \), \( y = 6 \):
\[
\frac{y}{x} = \frac{6}{4} = 1.5
\]

3. For \( x = 8 \), \( y = 8 \):
\[
\frac{y}{x} = \frac{8}{8} = 1
\]

The ratios are not constant (1.5, 1.5, 1), so the first set does not show a proportional relationship.

---

**Second set:**

\[
\begin{align*}
x & : 3, 6, 15 \\
y & : 4, 8, 20 \\
\end{align*}
\]

Calculating the ratios \( \frac{y}{x} \):

1. For \( x = 3 \), \( y = 4 \):
\[
\frac{y}{x} = \frac{4}{3} \approx 1.33
\]

2. For \( x = 6 \), \( y = 8 \):
\[
\frac{y}{x} = \frac{8}{6} = \frac{4}{3} \approx 1.33
\]

3. For \( x = 15 \), \( y = 20 \):
\[
\frac{y}{x} = \frac{20}{15} = \frac{4}{3} \approx 1.33
\]

The ratios are constant (\(\frac{4}{3} \approx 1.33\)), so the second set shows a proportional relationship.

---

**Conclusion:**
The second table shows a proportional relationship between \( x \) and \( y \), while the first table does not.