To solve this question, let's first understand the relationship between the slopes of two perpendicular lines.
Given:
- Line [tex]\( m \)[/tex] has a slope of [tex]\( \frac{p}{q} \)[/tex].
The key point to remember here is:
- The slope of a line that is perpendicular to another line is the negative reciprocal of the slope of the original line.
Here’s the step-by-step solution:
1. Original Slope: Determine the slope of the given line [tex]\( m \)[/tex]. The slope of line [tex]\( m \)[/tex] is given as [tex]\( \frac{p}{q} \)[/tex].
2. Negative Reciprocal: To find the slope of a line that is perpendicular to [tex]\( m \)[/tex], we need to find the negative reciprocal of [tex]\( \frac{p}{q} \)[/tex].
- Reciprocal of [tex]\( \frac{p}{q} \)[/tex]: The reciprocal of [tex]\( \frac{p}{q} \)[/tex] is [tex]\( \frac{q}{p} \)[/tex].
- Negative Reciprocal: The negative reciprocal of [tex]\( \frac{p}{q} \)[/tex] is [tex]\( -\frac{q}{p} \)[/tex].
3. Conclusion: Hence, the slope of the line that is perpendicular to line [tex]\( m \)[/tex] is [tex]\( -\frac{q}{p} \)[/tex].
Now, let's identify the correct choice from the given options:
A. [tex]\( \frac{a}{p} \)[/tex]
B. [tex]\( -\frac{s}{p} \)[/tex]
C. [tex]\( \frac{R}{8} \)[/tex]
D. [tex]\( -\frac{R}{8} \)[/tex]
None of the provided options directly match [tex]\( -\frac{q}{p} \)[/tex]. Therefore, based on the given choices, a specific determined slope that matches the pattern for slopes of lines is not directly listed. This indicates that the options provided might be a red herring, or we're simply confirming the correct form of the perpendicular slope without a precise match from designated letters in options.
