To determine which line is perpendicular to a line with a given slope, we need to understand that the slope of a line perpendicular to another is the negative reciprocal of the original line's slope.
Let's break down the steps:
1. Identify the slope of the given line:
- The given line has a slope of [tex]\(-\frac{1}{3}\)[/tex].
2. Find the slope of the perpendicular line:
- The slope of the perpendicular line is the negative reciprocal of [tex]\(-\frac{1}{3}\)[/tex].
- The reciprocal of [tex]\(-\frac{1}{3}\)[/tex] is [tex]\(-3\)[/tex]. Taking the negative of this, the slope of the perpendicular line becomes [tex]\(3\)[/tex].
3. Compare the slopes of the given lines:
- We need to identify which of the given lines (line MN, line AB, line EF, or line JK) has a slope of [tex]\(3\)[/tex].
After reviewing the information provided, we discover that the line [tex]\(EF\)[/tex] has a slope of exactly [tex]\(3\)[/tex]. Therefore, the line [tex]\(EF\)[/tex] is perpendicular to the given line with a slope of [tex]\(-\frac{1}{3}\)[/tex].
Hence, the line that is perpendicular to a line with a slope of [tex]\(-\frac{1}{3}\)[/tex] is:
[tex]\[
\text{line } EF
\][/tex]
