To find the correlation coefficient \( r \) for the given linear equation \( y = -\frac{3}{2}x + 6 \), we need to understand that this equation describes a perfect linear relationship between \( x \) and \( y \).
In this case, because it is an exact linear relationship, the correlation coefficient \( r \) will be:
- \( r = 1 \) if the relationship is positive,
- \( r = -1 \) if the relationship is negative,
- \( r = 0 \) if there is no linear relationship at all.
Since the slope of the line is negative (\(-\frac{3}{2}\)), the correlation coefficient for the linear equation \( y = -\frac{3}{2}x + 6 \) is:
\[ r = -1 \]
So, rounded to two decimal places:
\[ r = -1.00 \]
This indicates a perfect negative linear relationship between \( x \) and \( y \).
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