To determine the slope of a line that is perpendicular to the given line [tex]\( y = -\frac{1}{2}x + 5 \)[/tex], we need to follow these steps:
1. Identify the slope of the given line: The equation of the line is in the slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] represents the slope. For the line [tex]\( y = -\frac{1}{2}x + 5 \)[/tex], the slope [tex]\( m \)[/tex] is [tex]\(-\frac{1}{2} \)[/tex].
2. Determine the negative reciprocal of the slope: When two lines are perpendicular, 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].
- For the given slope [tex]\( m = -\frac{1}{2} \)[/tex], the negative reciprocal is calculated as follows:
[tex]\[
-\frac{1}{\left(-\frac{1}{2}\right)} = -(-2) = 2
\][/tex]
3. Conclusion: The slope of the line that is perpendicular to the line [tex]\( y = -\frac{1}{2}x + 5 \)[/tex] is [tex]\( 2 \)[/tex].
Therefore, the correct answer is [tex]\( 2 \)[/tex].
