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Answer :
Sure, let's find the slope of the line that is perpendicular to a given line with a slope of [tex]\(-\frac{5}{6}\)[/tex].
### Step-by-Step Solution:
1. Understand Slopes of Perpendicular Lines:
- Two lines are perpendicular if the product of their slopes is [tex]\(-1\)[/tex].
- This relationship can be written as:
[tex]\[
m_1 \times m_2 = -1
\][/tex]
- Here, [tex]\( m_1 \)[/tex] is the slope of the first line, and [tex]\( m_2 \)[/tex] is the slope of the line perpendicular to it.
2. Given Slope:
- The slope [tex]\( m_1 \)[/tex] of the given line is [tex]\(-\frac{5}{6}\)[/tex].
3. Find the Perpendicular Slope:
- Let [tex]\( m_2 \)[/tex] be the slope of the line perpendicular to the given line.
- According to the perpendicular slope relationship:
[tex]\[
m_1 \times m_2 = -1
\][/tex]
- Substituting the given slope into the equation:
[tex]\[
\left(-\frac{5}{6}\right) \times m_2 = -1
\][/tex]
- Solve for [tex]\( m_2 \)[/tex]:
[tex]\[
m_2 = \frac{-1}{-\frac{5}{6}} = \frac{1}{\frac{5}{6}} = \frac{6}{5}
\][/tex]
### Conclusion:
The slope of the line that is perpendicular to the given line with a slope of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
Now, to answer the question, we need to know which line (JK, LM, NO, PQ) has a slope of [tex]\(\frac{6}{5}\)[/tex]. Since the specific slopes of lines JK, LM, NO, and PQ are not provided in the problem, we would typically look at the equations of these lines to determine which one matches.
If additional information about these lines was provided, we could easily identify the correct line. Based on the given slopes, the answer matches the slope calculation of [tex]\(\frac{6}{5}\)[/tex].
### Step-by-Step Solution:
1. Understand Slopes of Perpendicular Lines:
- Two lines are perpendicular if the product of their slopes is [tex]\(-1\)[/tex].
- This relationship can be written as:
[tex]\[
m_1 \times m_2 = -1
\][/tex]
- Here, [tex]\( m_1 \)[/tex] is the slope of the first line, and [tex]\( m_2 \)[/tex] is the slope of the line perpendicular to it.
2. Given Slope:
- The slope [tex]\( m_1 \)[/tex] of the given line is [tex]\(-\frac{5}{6}\)[/tex].
3. Find the Perpendicular Slope:
- Let [tex]\( m_2 \)[/tex] be the slope of the line perpendicular to the given line.
- According to the perpendicular slope relationship:
[tex]\[
m_1 \times m_2 = -1
\][/tex]
- Substituting the given slope into the equation:
[tex]\[
\left(-\frac{5}{6}\right) \times m_2 = -1
\][/tex]
- Solve for [tex]\( m_2 \)[/tex]:
[tex]\[
m_2 = \frac{-1}{-\frac{5}{6}} = \frac{1}{\frac{5}{6}} = \frac{6}{5}
\][/tex]
### Conclusion:
The slope of the line that is perpendicular to the given line with a slope of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
Now, to answer the question, we need to know which line (JK, LM, NO, PQ) has a slope of [tex]\(\frac{6}{5}\)[/tex]. Since the specific slopes of lines JK, LM, NO, and PQ are not provided in the problem, we would typically look at the equations of these lines to determine which one matches.
If additional information about these lines was provided, we could easily identify the correct line. Based on the given slopes, the answer matches the slope calculation of [tex]\(\frac{6}{5}\)[/tex].
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