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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 find the negative reciprocal of the given slope. Here's how you can do it:
1. Understand the Concept: When two lines are perpendicular, the product of their slopes is [tex]\(-1\)[/tex]. This means that if you have a line with a slope [tex]\(m\)[/tex], a line perpendicular to it will have a slope that is the negative reciprocal of [tex]\(m\)[/tex].
2. Find the Negative Reciprocal: The negative reciprocal of a slope [tex]\(-\frac{5}{6}\)[/tex] is calculated by flipping the fraction and changing its sign. Therefore:
[tex]\[
\text{Negative reciprocal of } -\frac{5}{6} = \frac{6}{5}
\][/tex]
3. Result: The slope of the line that would be perpendicular to a line with slope [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
So, if line JK, line LM, line NO, or line PQ has a slope of [tex]\(\frac{6}{5}\)[/tex], that line would be perpendicular to the line with slope [tex]\(-\frac{5}{6}\)[/tex]. Check each line's slope to find the correct answer.
1. Understand the Concept: When two lines are perpendicular, the product of their slopes is [tex]\(-1\)[/tex]. This means that if you have a line with a slope [tex]\(m\)[/tex], a line perpendicular to it will have a slope that is the negative reciprocal of [tex]\(m\)[/tex].
2. Find the Negative Reciprocal: The negative reciprocal of a slope [tex]\(-\frac{5}{6}\)[/tex] is calculated by flipping the fraction and changing its sign. Therefore:
[tex]\[
\text{Negative reciprocal of } -\frac{5}{6} = \frac{6}{5}
\][/tex]
3. Result: The slope of the line that would be perpendicular to a line with slope [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
So, if line JK, line LM, line NO, or line PQ has a slope of [tex]\(\frac{6}{5}\)[/tex], that line would be perpendicular to the line with slope [tex]\(-\frac{5}{6}\)[/tex]. Check each line's slope to find the correct answer.
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