To determine which line is perpendicular to a given line with a slope of [tex]\(-\frac{5}{6}\)[/tex], we need to find the slope of the line that is perpendicular to it. Here’s a step-by-step explanation:
1. Identify the Slope of the Given Line:
The given line has a slope [tex]\( m_1 = -\frac{5}{6} \)[/tex].
2. Perpendicular Slope:
The slope of a line that is perpendicular to another line is the negative reciprocal of the original line's slope. To find the negative reciprocal:
- The negative reciprocal of a fraction [tex]\(\frac{a}{b}\)[/tex] is [tex]\(-\frac{b}{a}\)[/tex].
- For the given slope [tex]\( m_1 = -\frac{5}{6} \)[/tex], the negative reciprocal is:
[tex]\[
m_2 = -\left(-\frac{6}{5}\right) = \frac{6}{5}
\][/tex]
3. Simplify if Necessary:
We can convert [tex]\(\frac{6}{5}\)[/tex] to a decimal for clarity:
[tex]\[
\frac{6}{5} = 1.2
\][/tex]
4. Determine the Line with the Perpendicular Slope:
After identifying the slope [tex]\( 1.2 \)[/tex] (or [tex]\(\frac{6}{5}\)[/tex]), we need to check which one of the lines (JK, LM, NO, PQ) has a slope of [tex]\( 1.2 \)[/tex] to confirm it as the perpendicular line.
Unfortunately, the problem statement does not provide enough information to categorize the lines (JK, LM, NO, PQ) according to their slopes directly. If additional data were provided, such as specific coordinates for the points on each line, we could then calculate the slopes of each of those lines and identify which one matches the slope [tex]\( 1.2 \)[/tex].
However, based on the solution we have, the line that is perpendicular to the line with a slope of [tex]\(-\frac{5}{6}\)[/tex] has a slope of [tex]\(1.2\)[/tex]. You may need to compare this with given information (coordinates or slopes of the lines provided in a separate data set) to determine the exact line (JK, LM, NO, PQ) which matches the perpendicular criterion.
