To determine which line is perpendicular to a line with a slope of [tex]\(-\frac{1}{3}\)[/tex], we need to find the negative reciprocal of the given slope. The negative reciprocal of a number is found by taking the opposite sign (changing positive to negative or vice versa) and inverting the fraction.
1. Given slope of the original line: [tex]\(-\frac{1}{3}\)[/tex].
2. Calculate the negative reciprocal:
- Invert the fraction: [tex]\(\frac{1}{3}\)[/tex] becomes [tex]\(3\)[/tex] (since [tex]\( \frac{1}{\frac{1}{3}} = 3 \)[/tex]).
- Change the sign: Since the original slope is negative, the reciprocal will be positive. Thus, [tex]\(3\)[/tex] becomes just [tex]\(3\)[/tex].
Therefore, the slope of the line that is perpendicular to the line with slope [tex]\(-\frac{1}{3}\)[/tex] is [tex]\(3\)[/tex].
So, the line with a slope of [tex]\(3\)[/tex] is the line that is perpendicular to the line with a slope of [tex]\(-\frac{1}{3}\)[/tex].
In summary, without the actual slope values of lines MN, AB, EF, and JK provided, we conclude that any line from the given choices that has a slope of [tex]\(3\)[/tex] will be perpendicular to the line with the slope of [tex]\(-\frac{1}{3}\)[/tex].
