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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 slope. The negative reciprocal of a number is found by flipping the fraction and changing the sign.
1. Start with the original slope, which is [tex]\(-\frac{5}{6}\)[/tex].
2. Flip the fraction to get the reciprocal: [tex]\(\frac{6}{5}\)[/tex].
3. Change the sign to make it negative, which turns it into a positive: [tex]\(\frac{6}{5}\)[/tex].
This means the slope of a line that is perpendicular to the original line should be [tex]\(\frac{6}{5}\)[/tex].
Therefore, we are looking for the line with a slope of [tex]\(\frac{6}{5}\)[/tex] among the options given. The result from the calculation gives us [tex]\(1.2\)[/tex], which is the decimal form of the fraction [tex]\(\frac{6}{5}\)[/tex]. Make sure to check which of the lines, JK, LM, NO, or PQ, has this slope to identify the correct perpendicular line.
1. Start with the original slope, which is [tex]\(-\frac{5}{6}\)[/tex].
2. Flip the fraction to get the reciprocal: [tex]\(\frac{6}{5}\)[/tex].
3. Change the sign to make it negative, which turns it into a positive: [tex]\(\frac{6}{5}\)[/tex].
This means the slope of a line that is perpendicular to the original line should be [tex]\(\frac{6}{5}\)[/tex].
Therefore, we are looking for the line with a slope of [tex]\(\frac{6}{5}\)[/tex] among the options given. The result from the calculation gives us [tex]\(1.2\)[/tex], which is the decimal form of the fraction [tex]\(\frac{6}{5}\)[/tex]. Make sure to check which of the lines, JK, LM, NO, or PQ, has this slope to identify the correct perpendicular line.
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