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.
1. Understand the Slope Relationship:
- The slope of a line perpendicular to another line is the negative reciprocal of the given line's slope.
- The given slope is [tex]\(-\frac{5}{6}\)[/tex].
2. Calculate the Negative Reciprocal:
- The reciprocal of [tex]\(\frac{A}{B}\)[/tex] is [tex]\(\frac{B}{A}\)[/tex].
- Thus, the reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(-\frac{6}{5}\)[/tex].
- Taking the negative reciprocal, the negative of [tex]\(-\frac{6}{5}\)[/tex] gives us [tex]\(\frac{6}{5}\)[/tex].
3. Known Perpendicular Line Slope:
- 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].
4. Identifying the Correct Line:
- According to the problem data, Line [tex]\(JK\)[/tex] has a slope of [tex]\(\frac{6}{5}\)[/tex].
- Hence, Line [tex]\(JK\)[/tex] is the line that is perpendicular to the line with a slope of [tex]\(-\frac{5}{6}\)[/tex].
Therefore, among the options provided, line [tex]\(JK\)[/tex] is perpendicular to a line that has a slope of [tex]\(-\frac{5}{6}\)[/tex].
