To determine the slope of a line that is parallel to line \( m \), we should first recall a key property of parallel lines. Parallel lines have the same slope. So, the slope of any line that is parallel to line \( m \) will be exactly the same as the slope of line \( m \).
Given the information:
- Line \( m \) has a slope of \(\frac{p}{q}\), where \( p>0 \), \( q>0 \), and \( p \neq q \).
Since the question is asking for the slope of a line that is parallel to line \( m \), we need to identify the slope that matches \( \frac{p}{q} \).
The choices provided are:
A. \( \frac{q}{p} \)
B. \( \frac{p}{q} \)
C. \(-\frac{p}{q} \)
D. \(-\frac{q}{p} \)
From our understanding of parallel lines:
- Option A: \( \frac{q}{p} \) is the reciprocal of \( \frac{p}{q} \).
- Option C: \(-\frac{p}{q} \) is the negative of \( \frac{p}{q} \).
- Option D: \(-\frac{q}{p} \) is the negative reciprocal of \( \frac{p}{q} \).
- Option B: \( \frac{p}{q} \) is exactly the same as the slope of line \( m \).
Therefore, the correct choice that represents the slope of a line parallel to line \( m \) is:
B. [tex]\( \frac{p}{q} \)[/tex]
