Line [tex]$m$[/tex] has a [tex]$y$[/tex]-intercept of [tex]$c$[/tex] and a slope of [tex]$\frac{p}{q}$[/tex], where [tex]$p \ \textgreater \ 0$[/tex], [tex]$q \ \textgreater \ 0$[/tex], and [tex]$p \neq q$[/tex]. What is the slope of a line that is parallel to line [tex]$m$[/tex]?

A. [tex]$\frac{q}{p}$[/tex]
B. [tex]$\frac{p}{q}$[/tex]
C. [tex]$-\frac{p}{q}$[/tex]
D. [tex]$-\frac{q}{p}$[/tex]



Answer :

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]

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