To determine the slope of a line that is perpendicular to the line given by the equation [tex]\( y = 8x + 5 \)[/tex], we need to follow these steps:
1. Identify the slope of the given line:
The equation of the line is in slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] represents the slope. For the line [tex]\( y = 8x + 5 \)[/tex], the slope [tex]\( m \)[/tex] is 8.
2. Determine the slope of the perpendicular line:
The slope of any line perpendicular to another is the negative reciprocal of the slope of the given line.
- If the slope of the given line is [tex]\( m \)[/tex], the slope of the perpendicular line is [tex]\( -\frac{1}{m} \)[/tex].
3. Calculate the negative reciprocal:
The slope of the given line [tex]\( y = 8x + 5 \)[/tex] is 8. Therefore, the slope of the perpendicular line is:
[tex]\[
-\frac{1}{8}
\][/tex]
Thus, the slope of the line that is perpendicular to [tex]\( y = 8x + 5 \)[/tex] is [tex]\( -\frac{1}{8} \)[/tex].
From the provided options, the correct answer is:
[tex]\[
-\frac{1}{8}
\][/tex]
