The correlation coefficient \( r \) describes the strength and direction of a linear relationship between two variables. Given a linear equation of the form \( y = mx + b \), where \( m \) is the slope, the correlation coefficient can be evaluated.
Since the equation you provided is \( y = \frac{4}{3}x - 4 \), it has a positive slope (\(\frac{4}{3} \approx 1.33\)). In a perfect linear relationship, the \( r \) value can reach \( +1 \) for a positive correlation and \( -1 \) for a negative correlation.
However, to determine an exact correlation coefficient \( r \) for a specific dataset represented by this equation, we would need actual data points (values of \( x \) and \( y \)), which are not provided in your question.
In the context of this linear equation alone, since we are not given any data points to calculate the actual correlation, we can determine that:
- The slope is positive.
- The correlation coefficient can theoretically be as high as 1.00 (indicating perfect positive correlation) based on just the line.
If the context suggests that the relationship is perfectly linear based on the equation, then the correlation coefficient would be \( r = 1.00 \).
Thus, the answer among the provided options would be:
1.00.