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Answer :
To find a line that is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex], we need to determine the negative reciprocal of this slope. Here's how you can do it:
1. Understand the Concept: For two lines to be perpendicular, the product of their slopes must be [tex]\(-1\)[/tex].
2. Find the Negative Reciprocal: The slope of the given line is [tex]\(-\frac{5}{6}\)[/tex]. The negative reciprocal of a fraction is obtained by flipping the fraction (swapping the numerator and the denominator) and then changing the sign.
3. Calculate the Negative Reciprocal:
- Flip [tex]\(-\frac{5}{6}\)[/tex] to get [tex]\(-\frac{6}{5}\)[/tex].
- Change the sign to get [tex]\(\frac{6}{5}\)[/tex].
So, the slope of the line that is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
Now, among the options provided (line JK, line LM, line NO, line PQ), you would look for the line that has a slope of [tex]\(\frac{6}{5}\)[/tex]. If additional information about these lines were provided, such as equations or points they pass through, you could use it to determine which line has this slope.
1. Understand the Concept: For two lines to be perpendicular, the product of their slopes must be [tex]\(-1\)[/tex].
2. Find the Negative Reciprocal: The slope of the given line is [tex]\(-\frac{5}{6}\)[/tex]. The negative reciprocal of a fraction is obtained by flipping the fraction (swapping the numerator and the denominator) and then changing the sign.
3. Calculate the Negative Reciprocal:
- Flip [tex]\(-\frac{5}{6}\)[/tex] to get [tex]\(-\frac{6}{5}\)[/tex].
- Change the sign to get [tex]\(\frac{6}{5}\)[/tex].
So, the slope of the line that is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(\frac{6}{5}\)[/tex].
Now, among the options provided (line JK, line LM, line NO, line PQ), you would look for the line that has a slope of [tex]\(\frac{6}{5}\)[/tex]. If additional information about these lines were provided, such as equations or points they pass through, you could use it to determine which line has this slope.
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