Decide whether the table shows a proportional relationship between x and y.

Question

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 \( y \).