To determine which line is perpendicular to a line with a slope of [tex]\(-\frac{1}{3}\)[/tex], we need to find the slope of the perpendicular line first.
1. Understanding Perpendicular Slopes:
- If two lines are perpendicular to each other, then the slope of one line is the negative reciprocal of the slope of the other line.
- The negative reciprocal of a number [tex]\(a\)[/tex] is [tex]\(-\frac{1}{a}\)[/tex].
2. Given Slope:
- The slope of the original line is [tex]\(-\frac{1}{3}\)[/tex].
3. Finding the Perpendicular Slope:
- To find the slope of the line perpendicular to a line with a slope of [tex]\(-\frac{1}{3}\)[/tex], we take the negative reciprocal of [tex]\(-\frac{1}{3}\)[/tex].
- The negative reciprocal of [tex]\(-\frac{1}{3}\)[/tex] is:
[tex]\[
-\left(\frac{1}{-\frac{1}{3}}\right) = 3
\][/tex]
4. Conclusion:
- Therefore, the slope of the line that is perpendicular to the line with a slope of [tex]\(-\frac{1}{3}\)[/tex] is [tex]\(3\)[/tex].
Among the given options (line MN, line AB, line EF, line JK), we need additional information about the slopes of these lines to determine which of them specifically has a slope of 3. Without this information, we can't identify the exact name of the line from the given options.
The important takeaway is that the characteristic of the line perpendicular to a line with a slope of [tex]\(-\frac{1}{3}\)[/tex] is that its slope would be [tex]\(3\)[/tex].
