To solve the problem of finding a perpendicular line to a given line with a slope of [tex]\(-\frac{5}{6}\)[/tex], we need to follow these steps:
1. Identify the slope of the given line: The slope of the given line is [tex]\(-\frac{5}{6}\)[/tex].
2. Find the negative reciprocal: The slope of a line perpendicular to another line is the negative reciprocal of the original line’s slope.
- The negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is calculated as follows:
- The reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(-\frac{6}{5}\)[/tex].
- The negative of [tex]\(-\frac{6}{5}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
Therefore, the slope of the line that is perpendicular to the given line with a slope of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
Based on this result, you should check each option (line [tex]\(JK\)[/tex], line [tex]\(LM\)[/tex], line [tex]\(NO\)[/tex], line [tex]\(PQ\)[/tex]) to see which has a slope of [tex]\(\frac{6}{5}\)[/tex]. The line that has this slope will be the correct answer.
