Question

consider the line $y = -4 - 9x$. what is the slope of a line perpendicular to this line? what is the slope of a line parallel to this line? your answer slope of a perpendicular line: slope of a parallel line:

Explanation:

Step1: Identify the slope of the given line

The given line is \( y = -4 - 9x \), which can be rewritten in slope - intercept form \( y=mx + b \) (where \( m \) is the slope and \( b \) is the y - intercept) as \( y=-9x - 4 \). So the slope of the given line, \( m=-9 \).

Step2: Find the slope of a parallel line

Parallel lines have the same slope. So if a line is parallel to the line \( y = - 9x-4 \), its slope will be equal to the slope of the given line. So the slope of a parallel line is \( - 9 \).

Step3: Find the slope of a perpendicular line

If two lines with slopes \( m_1 \) and \( m_2 \) are perpendicular, then \( m_1\times m_2=-1 \). Let the slope of the perpendicular line be \( m_p \). We know that the slope of the given line \( m=-9 \). So we have the equation \( -9\times m_p=-1 \). Solving for \( m_p \), we get \( m_p=\frac{-1}{-9}=\frac{1}{9} \).

Answer:

Slope of a perpendicular line: \(\frac{1}{9}\)
Slope of a parallel line: \(-9\)