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Answer :
To determine the slope of a line perpendicular to another, we use the fact that the slopes of perpendicular lines are negative reciprocals of each other. Here is the step-by-step process:
1. The given line has a slope of
[tex]$$
m = -\frac{5}{6}.
$$[/tex]
2. The slope of a line perpendicular to one with slope [tex]$m$[/tex] is
[tex]$$
m_{\perp} = -\frac{1}{m}.
$$[/tex]
3. Substitute [tex]$m = -\frac{5}{6}$[/tex] into the formula:
[tex]$$
m_{\perp} = -\frac{1}{-\frac{5}{6}} = \frac{6}{5}.
$$[/tex]
4. The computed perpendicular slope is
[tex]$$
\frac{6}{5} = 1.2.
$$[/tex]
5. Among the provided options, the line that has this slope is line JK.
Thus, the line that is perpendicular to the line with slope [tex]$-\frac{5}{6}$[/tex] is line JK.
1. The given line has a slope of
[tex]$$
m = -\frac{5}{6}.
$$[/tex]
2. The slope of a line perpendicular to one with slope [tex]$m$[/tex] is
[tex]$$
m_{\perp} = -\frac{1}{m}.
$$[/tex]
3. Substitute [tex]$m = -\frac{5}{6}$[/tex] into the formula:
[tex]$$
m_{\perp} = -\frac{1}{-\frac{5}{6}} = \frac{6}{5}.
$$[/tex]
4. The computed perpendicular slope is
[tex]$$
\frac{6}{5} = 1.2.
$$[/tex]
5. Among the provided options, the line that has this slope is line JK.
Thus, the line that is perpendicular to the line with slope [tex]$-\frac{5}{6}$[/tex] is line JK.
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