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Answer :
To determine which line is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex], we need to understand the relationship between slopes of perpendicular lines.
Step 1: Identify the slope of the given line.
The slope of the given line is [tex]\(-\frac{5}{6}\)[/tex].
Step 2: Find the negative reciprocal.
The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope.
To find the negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex]:
- First, take the reciprocal of [tex]\(-\frac{5}{6}\)[/tex], which is [tex]\(-\frac{6}{5}\)[/tex].
- Then, change the sign to positive, resulting in [tex]\(\frac{6}{5}\)[/tex].
Step 3: Interpret the result.
The perpendicular slope is [tex]\(\frac{6}{5}\)[/tex]. This means any line with a slope of [tex]\(\frac{6}{5}\)[/tex] will be perpendicular to the original line with a slope of [tex]\(-\frac{5}{6}\)[/tex].
From the choices given (lines JK, LM, NO, PQ), you will be able to identify which line has a slope of [tex]\(\frac{6}{5}\)[/tex] as it will be perpendicular to the line with slope [tex]\(-\frac{5}{6}\)[/tex].
Step 1: Identify the slope of the given line.
The slope of the given line is [tex]\(-\frac{5}{6}\)[/tex].
Step 2: Find the negative reciprocal.
The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope.
To find the negative reciprocal of [tex]\(-\frac{5}{6}\)[/tex]:
- First, take the reciprocal of [tex]\(-\frac{5}{6}\)[/tex], which is [tex]\(-\frac{6}{5}\)[/tex].
- Then, change the sign to positive, resulting in [tex]\(\frac{6}{5}\)[/tex].
Step 3: Interpret the result.
The perpendicular slope is [tex]\(\frac{6}{5}\)[/tex]. This means any line with a slope of [tex]\(\frac{6}{5}\)[/tex] will be perpendicular to the original line with a slope of [tex]\(-\frac{5}{6}\)[/tex].
From the choices given (lines JK, LM, NO, PQ), you will be able to identify which line has a slope of [tex]\(\frac{6}{5}\)[/tex] as it will be perpendicular to the line with slope [tex]\(-\frac{5}{6}\)[/tex].
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