Question

consider the line $y = 5x - 1$. what is the slope of a line parallel to this line? what is the slope of a line perpendicular to this line? slope of a parallel line: \boxed{} slope of a perpendicular line: \boxed{}

Explanation:

Step1: Recall slope of parallel lines

Parallel lines have equal slopes. The given line is \( y = 5x - 1 \), which is in slope - intercept form \( y=mx + b \) where \( m \) is the slope. So the slope of the given line \( m = 5 \). Thus, the slope of a line parallel to it is also 5.

Step2: Recall slope of perpendicular lines

The slope of a line perpendicular to a line with slope \( m \) is the negative reciprocal, i.e., \( m_{\perp}=-\frac{1}{m} \). For \( m = 5 \), the negative reciprocal is \( -\frac{1}{5} \).

Answer:

Slope of a parallel line: \( 5 \)
Slope of a perpendicular line: \( -\frac{1}{5} \)