Without the image of the number line, it is difficult for me to determine the positions of the rational numbers m and n accurately. However, I can provide some general information based on the answer choices provided.
A. The value of n-m is positive: This would be true if n is greater than m on the number line. If n is to the right of m, then their difference, n-m, will be positive.
B. The value of n + m is positive: This would be true if both n and m are positive numbers. Adding two positive numbers will result in a positive sum. However, if either n or m is negative, the sum could be positive or negative, depending on the magnitudes of the numbers involved.
C. The value of n + m is negative: This would be true if both n and m are negative numbers. Adding two negative numbers will result in a negative sum. However, if either n or m is positive, the sum could be positive or negative, depending on the magnitudes of the numbers involved.
D. The value of -{n-m} is negative: This would be true if n is greater than m on the number line. If n is to the right of m, then their difference, n-m, will be positive. Taking the negative of a positive number will give a negative result.
In conclusion, without the specific positions of m and n on the number line, it is difficult to determine the correct statement. Please provide more information or clarify the question for a more accurate answer.