Question

consider the line $y = -2x - 1$. 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: slope of a parallel line:

Explanation:

Step1: Recall slope-intercept form

The given line is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the line \(y=-2x - 1\), the slope \(m\) of this line is \(-2\).

Step2: Find slope of parallel line

Parallel lines have the same slope. So, if a line is parallel to \(y=-2x - 1\), its slope will be equal to the slope of \(y=-2x - 1\), which is \(-2\).

Step3: Find slope of perpendicular line

The slope of a line perpendicular to a line with slope \(m\) is the negative reciprocal of \(m\). The formula for the slope of a perpendicular line \(m_{\perp}\) is \(m_{\perp}=-\frac{1}{m}\) (where \(m
eq0\)). For \(m = - 2\), the negative reciprocal is \(-\frac{1}{-2}=\frac{1}{2}\).

Answer:

Slope of a perpendicular line: \(\frac{1}{2}\)
Slope of a parallel line: \(-2\)