Question

Decide whether the table shows a proportional relationship between x and y.
x
2
4
7
10
y
4
16
49
100
Question content area bottom
Part 1
The table
▼
does not
does
show a proportional relationship between x and y.

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 consistent for each pair of values.

Let's calculate the ratio for each pair:

1. For \( x = 2 \) and \( y = 4 \):
\[
\frac{y}{x} = \frac{4}{2} = 2
\]

2. For \( x = 4 \) and \( y = 16 \):
\[
\frac{y}{x} = \frac{16}{4} = 4
\]

3. For \( x = 7 \) and \( y = 49 \):
\[
\frac{y}{x} = \frac{49}{7} = 7
\]

4. For \( x = 10 \) and \( y = 100 \):
\[
\frac{y}{x} = \frac{100}{10} = 10
\]

Now, we summarize the ratios:
- \( \frac{y}{x} = 2 \) (for \( x = 2 \))
- \( \frac{y}{x} = 4 \) (for \( x = 4 \))
- \( \frac{y}{x} = 7 \) (for \( x = 7 \))
- \( \frac{y}{x} = 10 \) (for \( x = 10 \))

These ratios are not consistent, so the table does not show a proportional relationship between \( x \) and \( y \).

Thus, the table **does not** show a proportional relationship between \( x \) and \( y \).