Question

consider the line y = 6x - 8. 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: slope of a perpendicular line:

Explanation:

Step1: Recall slope of parallel lines

Parallel lines have equal slopes. The given line is \( y = 6x - 8 \), which is in slope - intercept form \( y=mx + b \) where \( m \) is the slope. So the slope of the given line is \( m = 6 \). Thus, the slope of a line parallel to it is also \( 6 \).

Step2: Recall slope of perpendicular lines

If two lines are perpendicular, the product of their slopes is \( - 1 \). Let the slope of the perpendicular line be \( m_{\perp} \). We know that \( m\times m_{\perp}=-1 \), and \( m = 6 \). So \( 6\times m_{\perp}=-1 \), which gives \( m_{\perp}=-\frac{1}{6} \).

Answer:

Slope of a parallel line: \( 6 \)
Slope of a perpendicular line: \( -\frac{1}{6} \)