To determine the slope of a line that is perpendicular to another given line, we need to understand the relationship between their slopes.
The equation of the given line is [tex]\( y = -5x + 6 \)[/tex]. The coefficient of [tex]\( x \)[/tex] in this equation represents the slope of the line. Therefore, the slope of the given line is [tex]\( -5 \)[/tex].
When two lines are perpendicular, the slope of one line is the negative reciprocal of the slope of the other line. The reciprocal of a number is found by flipping the numerator and the denominator, and taking the negative of this value.
Let's start by finding the negative reciprocal of [tex]\( -5 \)[/tex]:
1. The slope of the original line is [tex]\( -5 \)[/tex].
2. The reciprocal of [tex]\( -5 \)[/tex] is [tex]\( \frac{-1}{-5} \)[/tex]. Simplifying, this gives:
[tex]\[
\frac{-1}{-5} = \frac{1}{5}
\][/tex]
Hence, the slope of a line perpendicular to the line [tex]\( y = -5x + 6 \)[/tex] is [tex]\( \frac{1}{5} \)[/tex].
So, the correct answer is:
D) [tex]\( \frac{1}{5} \)[/tex]
