Answer :
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.
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.
