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Answer :
To find a line that is perpendicular to a given line, we need to understand the relationship between their slopes. When two lines are perpendicular, the product of their slopes is [tex]\(-1\)[/tex]. This means if you have the slope of one line, the slope of the line perpendicular to it can be found using the formula:
[tex]\[ \text{perpendicular slope} = -\frac{1}{\text{original slope}} \][/tex]
In this case, the slope of the given line is [tex]\(-\frac{5}{6}\)[/tex]. To find the perpendicular slope:
1. Take the negative reciprocal of the original slope:
[tex]\[
\text{perpendicular slope} = -\frac{1}{(-\frac{5}{6})} = \frac{6}{5}
\][/tex]
Therefore, the line that is perpendicular to the line with a slope of [tex]\(-\frac{5}{6}\)[/tex] will have a slope of [tex]\(\frac{6}{5}\)[/tex].
To answer the question, identify which of the lines (JK, LM, NO, PQ) has this perpendicular slope of [tex]\(\frac{6}{5}\)[/tex]. You would choose the line from the options provided that has this slope as its defining characteristic.
[tex]\[ \text{perpendicular slope} = -\frac{1}{\text{original slope}} \][/tex]
In this case, the slope of the given line is [tex]\(-\frac{5}{6}\)[/tex]. To find the perpendicular slope:
1. Take the negative reciprocal of the original slope:
[tex]\[
\text{perpendicular slope} = -\frac{1}{(-\frac{5}{6})} = \frac{6}{5}
\][/tex]
Therefore, the line that is perpendicular to the line with a slope of [tex]\(-\frac{5}{6}\)[/tex] will have a slope of [tex]\(\frac{6}{5}\)[/tex].
To answer the question, identify which of the lines (JK, LM, NO, PQ) has this perpendicular slope of [tex]\(\frac{6}{5}\)[/tex]. You would choose the line from the options provided that has this slope as its defining characteristic.
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