Calvin's reasoning contains an error because he misunderstands the nature of the line \( y = 2 \). The equation \( y = 2 \) represents a horizontal line where \( y \) is always 2 for any value of \( x \). Therefore, any line parallel to \( y = 2 \) must also be a horizontal line, which means its equation will also have the form \( y = k \), where \( k \) is a constant.
In particular, if we want to find a line that is parallel to \( y = 2 \) and passes through the point \( (5, -1) \), we are looking for a horizontal line through the \( y \)-coordinate of the point \( -1 \).
Thus, the equation of the line parallel to \( y = 2 \) and passing through the point \( (5, -1) \) is simply:
\[ y = -1 \]
This line is horizontal and will never cross the line \( y = 2 \) because it maintains a constant \( y \)-value of \(-1\).
In summary, Calvin's assertion that he cannot find the equation using point-slope form is incorrect, as the concept of parallel lines in this context leads directly to identifying their constant \( y \)-value.