To determine the value of \( k \) and whether the transformation is a compression or a stretch, we can analyze the original ordered pair \((8, 21)\) and the transformed ordered pair \((2, 21)\).
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Identify the change in the x-values:
- Original x-value: \( 8 \)
- Transformed x-value: \( 2 \)
The change in the x-values can be expressed in terms of \( k \) as \( k \cdot 8 = 2 \).
To find \( k \), we rearrange this equation: \[ k = \frac{2}{8} = \frac{1}{4} \]
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Determine if it's a compression or a stretch:
- A value of \( k < 1 \) implies a compression (the x-values are made smaller).
- A value of \( k > 1 \) implies a stretch (the x-values are made larger).
Since \( k = \frac{1}{4} \), and it is less than 1, this indicates a compression.
In conclusion, the correct response is:
Start Fraction 1 over 4 End Fraction ; compression