When x = 2, 7, 11, …, y = 8, 28, 44, …, then x and y are in ________.

Answer

To determine the relationship between the sequences given for \( x \) and \( y \), we will analyze the values step-by-step.

### Step 1: Identify the sequences
The values of \( x \) are given as:
- \( x = 2, 7, 11, \ldots \)

The values of \( y \) are given as:
- \( y = 8, 28, 44, \ldots \)

### Step 2: Look for a pattern
Let's observe the relationship between the corresponding values of \( x \) and \( y \):
- For \( x = 2 \), \( y = 8 \)
- For \( x = 7 \), \( y = 28 \)
- For \( x = 11 \), \( y = 44 \)

### Step 3: Calculate the ratios
Now, we will check if there is a consistent ratio between \( x \) and \( y \):
- For \( x = 2 \):
\[ \frac{y}{x} = \frac{8}{2} = 4 \]
- For \( x = 7 \):
\[ \frac{y}{x} = \frac{28}{7} = 4 \]
- For \( x = 11 \):
\[ \frac{y}{x} = \frac{44}{11} = 4 \]

### Step 4: Conclusion
Since the ratio \( \frac{y}{x} \) is consistently equal to 4 for all given pairs, we can conclude that \( y \) is directly proportional to \( x \). This means that as \( x \) increases, \( y \) also increases in a consistent manner.

Thus, we can fill in the blank:
**x and y are in directly proportional.**

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