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

A. [tex]$\frac{2}{q}$[/tex]
B. [tex]$-\frac{q}{R}$[/tex]
C. [tex]$\frac{q}{R}$[/tex]
D. [tex]$-\frac{R}{Q}$[/tex]



Answer :

GinnyAnswer
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]

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