Question

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

Explanation:

Step1: Recall slope of parallel lines

Parallel lines have equal slopes. The given line is \( y = \frac{1}{5}x \), so its slope \( m_1=\frac{1}{5} \). Thus, the slope of a parallel line is also \( \frac{1}{5} \).

Step2: Recall slope of perpendicular lines

The product of slopes of two perpendicular lines is \( -1 \). Let the slope of the perpendicular line be \( m_2 \). Then \( m_1\times m_2=-1 \). Substituting \( m_1 = \frac{1}{5} \), we get \( \frac{1}{5}\times m_2=-1 \). Solving for \( m_2 \), we multiply both sides by 5: \( m_2=-5 \).

Answer:

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