To determine which line is perpendicular to a line with a slope of [tex]\(-\frac{1}{3}\)[/tex], we need to understand the relationship between the slopes of perpendicular lines. The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope.
1. Original Slope: The slope of the given line is [tex]\(-\frac{1}{3}\)[/tex].
2. Negative Reciprocal: To find the negative reciprocal:
- First, take the reciprocal of [tex]\(-\frac{1}{3}\)[/tex]. The reciprocal of [tex]\(-\frac{1}{3}\)[/tex] is [tex]\(-3\)[/tex], because [tex]\(\frac{1}{-\frac{1}{3}} = -3\)[/tex].
- Then, take the negative of [tex]\(-3\)[/tex], which is [tex]\(3\)[/tex].
Thus, the slope of the line that is perpendicular to the original line is [tex]\(3\)[/tex].
Since we are asked which specific line (MN, AB, EF, JK) is perpendicular, and we know the perpendicular slope is [tex]\(3\)[/tex], any one of the mentioned lines with a slope of [tex]\(3\)[/tex] will be the correct answer. Given the context and without further information about the slopes of the named lines, we have determined the perpendicular slope is indeed [tex]\(3\)[/tex].
Therefore, a line that is perpendicular to the given line (with slope [tex]\(-\frac{1}{3}\)[/tex]) must have a slope of [tex]\(3\)[/tex].
