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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 perpendicular to line [tex]\( m \)[/tex]?

A. [tex]\( -\frac{p}{q} \)[/tex]

B. [tex]\( -\frac{q}{p} \)[/tex]

C. [tex]\(\frac{\varepsilon}{p}\)[/tex]

D. [tex]\(\frac{p}{q}\)[/tex]

Sagot :

GinnyAnsweridn
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]
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