To determine which line is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex], we need to understand the concept of perpendicular slopes.
1. Original Slope Identification:
- We have an original line with a slope of [tex]\(-\frac{5}{6}\)[/tex].
2. Negative Reciprocal:
- The slope of a line that is perpendicular to another line is the negative reciprocal of the original slope.
- To find the negative reciprocal, you flip the fraction and change the sign.
3. Calculation:
- The original slope is [tex]\(-\frac{5}{6}\)[/tex].
- The reciprocal of [tex]\(-\frac{5}{6}\)[/tex] is [tex]\(-\frac{6}{5}\)[/tex], and the negative of that is [tex]\(\frac{6}{5}\)[/tex].
Therefore, 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].
Given that the numerical representation of [tex]\(\frac{6}{5}\)[/tex] is 1.2, the slope of the perpendicular line is 1.2.
Thus, the line that is perpendicular to a line with a slope of [tex]\(-\frac{5}{6}\)[/tex] has a slope of 1.2.
