To find the slope of a line that is perpendicular to a given line, we need to use the concept of negative reciprocals. The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line.
1. We are given that line [tex]\( m \)[/tex] has a slope of [tex]\(\frac{R}{q}\)[/tex].
2. To find the slope of the line that is perpendicular to line [tex]\( m \)[/tex], we need to take the negative reciprocal of [tex]\(\frac{R}{q}\)[/tex].
Let's break this process down:
Step 1: Identify the slope of the given line.
- The slope of line [tex]\( m \)[/tex] is [tex]\(\frac{R}{q}\)[/tex].
Step 2: Find the negative reciprocal of the slope.
- The reciprocal of [tex]\(\frac{R}{q}\)[/tex] is [tex]\(\frac{q}{R}\)[/tex].
- Taking the negative of this reciprocal, we have [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].
So, the correct answer is:
[tex]\[ \boxed{-\frac{q}{R}} \][/tex]
