To solve this problem, let's start by examining the given information and properties of perpendicular lines.
1. Understand the slope of line [tex]\( m \)[/tex]:
- We are given that the slope of line [tex]\( m \)[/tex] is [tex]\(\frac{R}{q}\)[/tex].
2. Determine the slope of a perpendicular line:
- Two lines are perpendicular if the product of their slopes is [tex]\(-1\)[/tex].
- If the slope of line [tex]\( m \)[/tex] is [tex]\(\frac{R}{q}\)[/tex], then the slope of the line that is perpendicular to [tex]\( m \)[/tex] must be the negative reciprocal of [tex]\(\frac{R}{q}\)[/tex].
3. Calculate the negative reciprocal:
- To find the negative reciprocal, we take the reciprocal of [tex]\(\frac{R}{q}\)[/tex] and then multiply by -1.
- The reciprocal of [tex]\(\frac{R}{q}\)[/tex] is [tex]\(\frac{q}{R}\)[/tex].
- Multiplying by -1 gives us [tex]\(-\frac{q}{R}\)[/tex].
Therefore, the slope of a line that is perpendicular to line [tex]\( m \)[/tex] is [tex]\(-\frac{q}{R}\)[/tex].
Given the multiple-choice options:
- A. [tex]\(\frac{2}{q}\)[/tex]
- B. [tex]\(-\frac{q}{p}\)[/tex]
- C. [tex]\(\frac{q}{p}\)[/tex]
- D. [tex]\(-\frac{R}{q}\)[/tex]
The correct answer is not listed explicitly in the options provided above. As per the true mathematical solution based on perpendicular slopes, though, the correct perpendicular slope to [tex]\(\frac{R}{q}\)[/tex] is indeed:
[tex]\[
-\frac{q}{R}
\][/tex]
