To solve this problem, we need to find the slope of a line that is perpendicular to the given line \( y = -\frac{1}{2}x - 68 \).
1. Identify the slope of the given line:
The equation of the line is given in slope-intercept form \( y = mx + b \), where \( m \) is the slope.
For the line \( y = -\frac{1}{2}x - 68 \), the slope \( m \) is \( -\frac{1}{2} \).
2. Find the negative reciprocal:
The slope of a line perpendicular to another line is the negative reciprocal of the given slope.
- The reciprocal of \( -\frac{1}{2} \) is \( -2 \) (reciprocal changes the numerator and denominator and flips the sign).
- The negative reciprocal of \( -\frac{1}{2} \) is therefore \( 2 \).
So, the slope of the perpendicular line is \( 2 \).
Given the multiple choices, the correct answer is:
d.) [tex]\( 2 \)[/tex]
