To determine the slope of a line that is perpendicular to a given line, we use the concept of negative reciprocals. If you have the slope of a line, the slope of the line that is perpendicular to it is the negative reciprocal of that original slope.
Given:
- The slope of the original line is [tex]\( -2 \)[/tex].
To find the perpendicular slope:
1. First, take the given slope [tex]\( -2 \)[/tex].
2. Find the reciprocal of the slope. The reciprocal of [tex]\( -2 \)[/tex] is [tex]\( -\frac{1}{2} \)[/tex].
3. Then, negate the reciprocal. Negating [tex]\( -\frac{1}{2} \)[/tex] gives us [tex]\( \frac{1}{2} \)[/tex].
Therefore, the slope of the line that is perpendicular to the line with a slope of [tex]\( -2 \)[/tex] is [tex]\( \frac{1}{2} \)[/tex].
The answer is [tex]\( \frac{1}{2} \)[/tex].
