To find the value of \( k \) that describes the transformation from the original ordered pair \( (8, 2) \) to the transformed ordered pair \( (2, 2) \), we need to analyze how the \( x \)-coordinates of these pairs relate.
- The original \( x \)-coordinate is 8.
- The transformed \( x \)-coordinate is 2.
The transformation can usually be described as either a horizontal or vertical scaling or translation. In this case, the transformation involves a scaling factor \( k \) applied to the \( x \)-coordinate:
\[ kx = 2 \]
Substituting the original \( x \)-coordinate:
\[ k \cdot 8 = 2 \]
Now, to solve for \( k \), we divide both sides by 8:
\[ k = \frac{2}{8} = \frac{1}{4} \]
Thus, the value of \( k \) is:
\[ \boxed{\frac{1}{4}} \]