To determine the value of \( k \) in the context of a horizontal stretch or compression, we can use the formula relating the original ordered pair \((x, y)\) to the transformed ordered pair \((kx, y)\).
The original ordered pair is \((8, 2)\) and the transformed ordered pair is \((2, 2)\).
From the transformation:
- The \( y \)-value remains the same, indicating that no vertical transformation occurred.
- The \( x \)-value changes from \( 8 \) to \( 2 \).
We can set up the equation based on the transformation in \( x \):
\[ kx = 2 \] where \( x = 8 \). Thus, substituting for \( x \):
\[ k \cdot 8 = 2 \]
Now, solve for \( k \):
\[ k = \frac{2}{8} = \frac{1}{4} \]
Therefore, the value of \( k \) is \( \frac{1}{4} \).
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