Answer :

To determine which line is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex], we need to find the slope of the perpendicular line.

Here's how you can find the slope of a line that's perpendicular to another line:

1. The perpendicular slope is the negative reciprocal of the given slope. This means you flip the fraction and change the sign.

2. Given the original slope is [tex]\(-\frac{5}{6}\)[/tex], the steps are:

- First, find the reciprocal of [tex]\(-\frac{5}{6}\)[/tex]. The reciprocal is [tex]\(-\frac{6}{5}\)[/tex].

- Then, change the sign to get the negative reciprocal. So, [tex]\(-\frac{6}{5}\)[/tex] becomes [tex]\(\frac{6}{5}\)[/tex].

Thus, the slope of the perpendicular line is [tex]\(\frac{6}{5}\)[/tex]. We need to check which of the lines (JK, LM, NO, PQ) has this slope. Without specific details about these lines, the slope [tex]\(\frac{6}{5}\)[/tex] is what you should be looking for to determine which line is perpendicular to the given one.

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