Question

for the line given by, y = - 2x, find the slope of a line that is: a) parallel to the given line: m_parallel = b) perpendicular to the given line: m_perpendicular = note: you can earn partial credit on this problem. you have attempted this problem 0 times. you have unlimited attempts remaining. preview my answers submit answers

Explanation:

Step1: Recall slope - parallel line relationship

Parallel lines have equal slopes. The given line is \(y = - 2x\), and its slope \(m=-2\). So the slope of a line parallel to it, \(m_{parallel}=-2\).

Step2: Recall slope - perpendicular line relationship

The product of the slopes of two perpendicular lines is \(- 1\). Let the slope of the given line be \(m=-2\) and the slope of the perpendicular line be \(m_{perpendicular}\). Then \(-2\times m_{perpendicular}=-1\). Solving for \(m_{perpendicular}\), we get \(m_{perpendicular}=\frac{1}{2}\).

Answer:

a) \(m_{parallel}=-2\)
b) \(m_{perpendicular}=\frac{1}{2}\)