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Answer :
To find a line that is perpendicular to a given line with a slope of [tex]\(-\frac{5}{6}\)[/tex], we need to understand that the slope of a perpendicular line is the negative reciprocal of the original slope.
Here's how to find the negative reciprocal:
1. Original Slope: The original slope is [tex]\(-\frac{5}{6}\)[/tex].
2. Reciprocal Step: Take the reciprocal of the slope: Flip the fraction, changing [tex]\(-\frac{5}{6}\)[/tex] to [tex]\(-\frac{6}{5}\)[/tex].
3. Negative Step: Change the sign. Since the original slope is negative, the negative reciprocal will be positive. Therefore, the perpendicular slope becomes [tex]\(\frac{6}{5}\)[/tex].
The slope of the line that is perpendicular to the given line is [tex]\(\frac{6}{5}\)[/tex], or as a decimal, it is 1.2. Therefore, the line in the list provided that has this slope, if given, would be the line perpendicular to line with slope [tex]\(-\frac{5}{6}\)[/tex]. You'd need to check the options for which line has this slope of 1.2.
Here's how to find the negative reciprocal:
1. Original Slope: The original slope is [tex]\(-\frac{5}{6}\)[/tex].
2. Reciprocal Step: Take the reciprocal of the slope: Flip the fraction, changing [tex]\(-\frac{5}{6}\)[/tex] to [tex]\(-\frac{6}{5}\)[/tex].
3. Negative Step: Change the sign. Since the original slope is negative, the negative reciprocal will be positive. Therefore, the perpendicular slope becomes [tex]\(\frac{6}{5}\)[/tex].
The slope of the line that is perpendicular to the given line is [tex]\(\frac{6}{5}\)[/tex], or as a decimal, it is 1.2. Therefore, the line in the list provided that has this slope, if given, would be the line perpendicular to line with slope [tex]\(-\frac{5}{6}\)[/tex]. You'd need to check the options for which line has this slope of 1.2.
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