To determine the value of \( k \) in the context of the transformation from the ordered pair (2, 9) to (6, 9), we need to see how the \( x \)-coordinate changes.
The original \( x \)-coordinate is 2, and after the transformation, it becomes 6. You can express this transformation using \( k \) such that:
\[ k \cdot x_{\text{original}} = x_{\text{transformed}} \]
Substituting in the values we have:
\[ k \cdot 2 = 6 \]
Solving for \( k \):
\[ k = \frac{6}{2} = 3 \]
Now let's determine whether this represents a stretch or a compression.
When \( k > 1 \), the transformation results in a stretch. When \( 0 < k < 1 \), it results in a compression. Since \( k = 3 \) and it is greater than 1, this indicates a stretch.
Thus, the correct identification is:
3; stretch.