To determine the slope of a line that is perpendicular to a given line, we need to find the negative reciprocal of the slope of the original line.
Given that the slope of the original line is [tex]\(-\frac{5}{6}\)[/tex], we will follow these steps to find the slope of the perpendicular line:
1. Identify the slope of the original line: The slope of the given line is [tex]\(-\frac{5}{6}\)[/tex].
2. Calculate the negative reciprocal of the original slope:
- The reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(-\frac{6}{5}\)[/tex].
- The negative reciprocal would be the negative of [tex]\(-\frac{6}{5}\)[/tex], which is [tex]\(\frac{6}{5}\)[/tex].
So, the slope of the line that is perpendicular to the original line with slope [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
Thus, any line that has a slope of [tex]\(\frac{6}{5}\)[/tex] is perpendicular to the line with the slope of [tex]\(-\frac{5}{6}\)[/tex]. The specific line (whether it's line JK, line LM, line NO, or line PQ) needs to be identified based on having this slope.
